Emission source and method of forming the same

ABSTRACT

In various embodiments, an emission source may be provided. The emission source may also include a gain medium including a halide semiconductor material. The emission source may further include a pump source configured to provide energy to the gain medium.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority of U.S. application No.61/876,940 filed Sep. 12, 2013, the contents of it being herebyincorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

Various aspects of this disclosure relate to emission sources andmethods of forming the same.

BACKGROUND

A laser (acronym for light amplification by stimulated emission ofradiation) emits coherent light through a process of opticalamplification via the stimulated emission of electromagnetic radiation.Lasers or coherent light sources have many important applications whichform the cornerstones of our modern society. These range from fastinformation processing and telecommunications; optical data storage;bio-imaging; medical diagnostic and phototherapy to scientific researchand defence applications. The demands for such applications continue togrow with Mankind's relentless pursuit of sustainable growth.

The heart of a laser is its gain medium—a material that makes lightstronger or permits optical amplification to occur. Opticalamplification, also known as gain occurs when the gain materialtransfers part of its energy to light and makes the light more intenseand in phase. Typical gain media include crystals (e.g., neodymium-dopedyttrium aluminum garnet (Nd:YAG), titanium doped aluminum oxide(Ti:Sapphire) and neodymium-doped yttrium orthovanadate (Nd:YVO₄) etc.)and high quality semiconductors (e.g. gallium arsenide (GaAs) andaluminum gallium arsenide (Al_(x)Ga_((1-x))As) etc). These gain mediatypically operate in the infrared (IR) region of the electromagneticspectrum. To obtain wavelengths in the ultraviolet (UV) or visible (VIS)region, wavelength conversion of IR photons with nonlinear crystals isperformed. For example, in the modest hand-held laser pointer, the greenlight is generated indirectly—beginning with an AlGaAs laser diode (808nm) pumping a NdYVO₄ crystal to generate 1064 nm photons which are thenfrequency doubled by a KTP crystal to 532 nm. It is important to notethe stringent conditions needed to prepare the high quality, crystallinegain materials, which involve costly high temperature growth andprocessing. For example, GaAs and Al_(x)Ga_((1-x))As heterostructuresrequire expensive elevated temperature and high vacuum growth techniquessuch as chemical vapor deposition (CVD) and molecular beam epitaxy(MBE).

SUMMARY

In various embodiments, an emission source may be provided. The emissionsource may also include a gain medium including a halide semiconductormaterial. The emission source may further include a pump sourceconfigured to provide energy to the gain medium.

In various embodiments, a method of forming an emission source may beprovided. The method may include providing a gain medium including ahalide semiconductor material. The method may also include providing apump source configured to provide energy to the gain medium.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood with reference to the detaileddescription when considered in conjunction with the non-limitingexamples and the accompanying drawings, in which:

FIG. 1 is a schematic showing a cross-sectional side view of an emissionsource according to various embodiments.

FIG. 2A is a schematic showing a cross-sectional side view of anemission source according to various embodiments.

FIG. 2B shows a schematic showing a cross-sectional side view of anemission source according to various embodiments.

FIG. 2C shows a schematic showing a cross-sectional side view of anemission source according to various alternate embodiments.

FIG. 2D shows a schematic showing a perspective view an emission sourceaccording to various alternate embodiments.

FIG. 2E shows a schematic showing a cross-sectional side view of theemission source of FIG. 2D according to various embodiments.

FIG. 2F shows a schematic showing a cross-sectional side view of anemission source according to various other embodiments.

FIG. 2G shows a schematic showing a cross-sectional side view of anemission source according to various other embodiments.

FIG. 2H shows a schematic showing a cross-sectional side view of anemission source according to various other embodiments.

FIG. 2I shows a schematic showing a cross-sectional side view of anemission source according to various other embodiments.

FIG. 3 shows a schematic of a method of forming an emission sourceaccording to various embodiments.

FIG. 4A is a plot of a comparison of the amplified spontaneous emission(ASE) profile in relation to the absorption and spontaneous emission(SE)/photoluminescence profile for CH₃NH₃PbI₃.

FIG. 4B shows a plot of a typical time resolved photoluminescence (TRPL)decay transients following photo-excitation with pump fluence below (˜10μJ cm⁻²) and above (˜13 μJ cm⁻²) the ASE threshold (i.e., 12±2 μJ cm⁻²).

FIG. 4C is a streak camera image 400 c of spectrum against time(collected over a time window of 460 ps) for below ASE thresholdfluence.

FIG. 4D is a streak camera image 400 d of spectrum against time(collected over a time window of 460 ps) for above ASE thresholdfluence.

FIG. 5A is a plot showing the real part (n) and imaginary part orextinction coefficient (k) of the complex refractive index.

FIG. 5B shows a schematic of the of a gain medium under simulationconditions according to various embodiments.

FIG. 5C is a schematic showing intensity distributions in the y-z planeof structures of light polarized parallel to the structure surface.

FIG. 6A is a plot of pump fluence dependent photoluminescence (PL)spectra at 6K.

FIG. 6B is a plot of pump fluence dependent photoluminescence (PL)intensity at 6K.

FIG. 6C is a plot showing time resolved photoluminescence (TRPL) TRPLdecay transients for quartz/CH₃NH₃PbI₃ (65 nm) and quartz/CH₃NH₃PbI₃ (65nm)/PCBM(45 nm) films in vacuum following excitation at 600 nm (1 KHz,150 fs, ˜1 μJ cm⁻²).

FIG. 7A is a schematic of a solar cell according to various embodiments.

FIG. 7B is a plot showing the current density J (mA cm⁻²) under A 1.5(100 mW/cm²) illumination.

FIG. 7C is a plot of photoluminescence (PL) intensity (arbitrary units)as a function of pump fluence (μ J cm⁻²) showing amplified spontaneousemission (ASE) threshold of the solar cell configuration.

FIG. 7D is a plot of the ASE spectrum.

FIG. 7E is a plot showing ASE photostability measured under ambientconditions of the device (Excited with 600 nm, 1 KHz, 50 fs laserpulses, ˜20 μJ cm⁻²).

FIG. 7F is a photo showing a demonstration of green ASE from CH₃NH₃PbBr₃deposited on PET substrates pumped using two-photon absorption at 800nm.

FIG. 8A is a plot showing steady-state photoluminescence (PL) emissionspectra from a 65-nm-thick CH₃NH₃PbI₃ film photoexcited using 600 nm,150 fs and 1 kHz pump pulses with increasing pump fluence (per pulse).

FIG. 8B is a plot showing the corresponding time resolvedphotoluminescence (TRPL) intensity measured at 788±10 nm.

FIG. 8C is a plot full width at half maximum (FWHM) of the emission peakand average transient photoluminescence lifetime (τ_(PL)) as a functionof the pump fluence.

FIG. 8D is a plot showing photoluminescence intensity as a function ofpump fluence.

FIG. 9A is a plot showing photoluminescence quantum yield (PLQY) (inpercentage or %) dependence on pump fluence (in μJ cm⁻²).

FIG. 9B is a plot showing room temperature variable stripe length (VSL)measurements of the CH₃NH₃PbI₃ films and fitted using the respectivemethods used for solution processed colloidal quantum dots thin films.

FIG. 9C is a plot showing room temperature variable stripe length (VSL)measurements of the CH₃NH₃PbI₃ films and fitted using the respectivemethods used for organic thin films.

FIG. 10A is a plot showing room temperature lasing from CH₃NH₃PbI₃single crystals from dropcasted films.

FIG. 10B is an optical micrograph of the crystal.

FIG. 10C is a plot showing the lasing data fitted to 5 peaks.

FIG. 10D is a plot showing photoluminescence (PL) intensity as afunction of photon-generated exciton density within the low pump fluencerange.

FIG. 11A is a plot showing the time-integrated PL spectra of CH₃NH₃PbI₃and CH₃NH₃PbI₃/([6,6]-phenyl-C61-butyric acid methyl ester (PCBM).

FIG. 11B is a plot showing the time-resolved photoluminescence (TRPL)decay transients for quartz/CH₃NH₃PbI₃ (about 1.3 μJ cm⁻²),quartz/CH₃NH₃PbI₃/PCBM (about 1.3 μJ cm⁻² and about 17 μJ cm⁻²) films invacuum following excitation at 600 nm (1 kHz, 150 fs).

FIG. 11C is a plot of the pump fluence-dependent photoluminescencespectra of quartz/CH₃NH₃PbI₃ (65 nm)/PCBM film.

FIG. 11D is a plot of the photoluminescence intensity ofquartz/CH₃NH₃PbI₃ (65 nm)/PCBM film.

FIG. 12A is a plot showing shot-dependent ASE intensity of thesolution-processed CH₃NH₃PbI₃ film with over 9×10⁷ laser excitationshots at 600 nm (1 kHz, 50 fs, ˜18 μJ cm⁻²) performed at roomtemperature.

FIG. 12B is a plot showing shot-dependent ASE intensity of the solutionprocessed CH₃NH₃PbI₃ and CH₃NH₃PbI₃/PCBM films over 7×10⁶ at 600 nm (1KHz, 50 fs, 14 μJ/cm²) under room temperature.

FIG. 12C is a plot showing the PL spectrum at 10 K. The dotted lines arethe deconvolved Gaussian peaks.

FIG. 12D is a plot showing wide wavelength tunability of ASE wavelengthsfrom low-temperature solution-processed organic-inorganic halidesemiconductor films fabricated by mixing the precursor solutions.

FIG. 13A is a plot showing the time-integrated PL spectra measured at760±10 nm for quartz/CH₃NH₃PbI₃(65 nm), quartz//CH₃NH₃PbI₃ (65 nm)/PCBM(indicated by 1304 a), quartz/CH₃NH₃PbI₃(65 nm)/Spiro-OMeTAD films invacuum following excitation at 600 nm (1 KHz, 150 fs, 1.3 μJ/cm2).

FIG. 13B is a plot showing TRPL decay transients measured at 760±10 nmfor quartz/CH₃NH₃PbI₃(65 nm), quartz/CH₃NH₃PbI₃(65 nm)/PCBM,quartz/CH₃NH₃PbI₃(65 nm)/Spiro-OMeTAD films in vacuum followingexcitation at 600 nm (1 KHz, 150 fs, 1.3 μJ/cm2).

FIG. 13C is a plot of exciton diffusion length as a function of PLlifetime quenching ratios.

FIG. 14A is an illustration showing the absorbance and transmissionspectra of CH₃NH₃PbI₃, CH₃NH₃PbI₃/PCBM, CH₃NH₃PbI₃/Spiro-OMeTAD.

FIG. 14B is an illustration 1400 b showing normalized bleaching kineticsfor films in vacuum following excitation at 600 nm (1 KHz, 150 fs, 1.3μJ/cm²).

FIG. 15A is an illustration of normalized bleaching kinetics in shorttime range showing the inter-valence band hot hole cooling forCH₃NH₃PbI₃ (in vacuum) following excitation.

FIG. 15B is a schematic illustrating the hot hole cooling and chargerecombination within CH₃NH₃PbI₃ and charge separation at theCH₃NH₃PbI₃/PCBM and CH₃NH₃PbI₃/Spiro-OMeTAD interfaces.

FIG. 16 is a schematic of the energy levels of the heterojunctions anddepiction of the exciton generation, diffusion and quenching processesin the respective bilayers.

FIG. 17 is a plot showing step profiles of the thickness of theCH₃NH₃PbI₃, CH₃NH₃PbI₃/PCBM and CH₃NH₃PbI₃/Spiro-OMeTAD films.

FIG. 18 is a cross-sectional transmission electron microscopy image of atypical trilayer showing the clear interfaces between the perovskite andthe electron and hole acceptor layers.

FIG. 19 is a plot of absorption coefficient of CH₃NH₃PbI₃ as a functionof wavelength.

FIG. 20 is a schematic showing 4 possible scenarios for the two peaks(480 nm and 760 nm) observed in the linear absorption and TA spectra.

FIG. 21 is a plot showing normalized probe wavelength dependent kineticsfor CH₃NH₃PbI₃ film in vacuum following excitation at 600 nm (0.7μJ/cm²).

FIG. 22 is a plot showing normalized pump fluence dependent kinetics at760 nm for CH₃NH₃PbI₃ film vacuum following excitation at 600 nm.

FIG. 23 is an illustration showing pump fluence dependent dynamics forCH₃NH₃PbI₃ and CH₃NH₃PbI₃ in vacuum.

FIG. 24 is a plot showing pump fluence dependent relative PL quantumyield with 600 nm, 150 fs and 1 KHz laser pulse excitation.

FIG. 25 is a table showing relative photoluminescence (PL) quantum yield(ç_(PL)), PL decay time (τ_(PL)), TA decay time (τ_(TA)) and theestimated charge transfer time (τ_(CT)) from the TA results.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawingsthat show, by way of illustration, specific details and embodiments inwhich the invention may be practiced. These embodiments are described insufficient detail to enable those skilled in the art to practice theinvention. Other embodiments may be utilized and structural, and logicalchanges may be made without departing from the scope of the invention.The various embodiments are not necessarily mutually exclusive, as someembodiments can be combined with one or more other embodiments to formnew embodiments.

In order that the invention may be readily understood and put intopractical effect, particular embodiments will now be described by way ofexamples and not limitations, and with reference to the figures.

Various embodiments relate to low temperature, solution processable highcrystallinity gain media. Various embodiments not only reduce theproduction costs but also permit application of such solutionprocessable gain media to a much wider range of resonator designscompatible for on-chip integration.

FIG. 1 is a schematic 100 showing an emission source according tovarious embodiments. The emission source may also include a gain medium102, the gain medium 102 including a halide semiconductor material. Theemission source may further include a pump source 104 configured toprovide energy to the gain medium 102.

In other words, the emission source may include a gain medium 102 madeof a halide semiconductor material. The emission source may furtherinclude a pump source 104 to provide energy to the gain medium 102.

The halide semiconductor material may also be referred to as a halidesemiconductor. The halide semiconductor material may be or may include ahalide perovskite material. The halide perovskite material may includean organic-inorganic perovskite material. The halide perovskite materialmay be or may include a three dimensional halide perovskite material.The halide perovskite material may also be referred to as perovskitematerial. In general, the halide semiconductor material may be or mayinclude a three dimensional halide semiconductor material.

FIG. 2A is a schematic 200 a showing a cross-sectional side view anemission source according to various embodiments. The emission sourcemay also include a gain medium 202, the gain medium 202 including ahalide semiconductor material such as a halide perovskite material. Theemission source may further include a pump source 204 configured toprovide energy to the gain medium 202.

In various embodiments, the emission source may be a source forproviding amplified spontaneous emission (ASE). In addition, theemission may additionally or alternatively provide spontaneous emission(SE), and/or stimulated emission (laser).

The pump source 204 may be configured to supply energy to the gainmedium through a process called pumping. In various embodiments, thepump source 204 may be or may include an optical source configured toprovide light as energy to the gain medium 202. The optical source may aflash lamp or by a laser. The optical source may emit light of awavelength different from the light which the emission source generatesor emit.

In various alternate embodiments, the pump source 204 may be or mayinclude an electrical source configured to provide electrical energy tothe gain medium 202. The electrical source may be configured to supply acurrent to the gain medium 202.

As shown in FIG. 2A, the emission source may include a resonant cavity206. The gain medium 202 may be arranged within the resonant cavity 206.The resonant cavity 206 may be an open cavity. In other words, the gainmedium 202 may be arranged to couple with a resonant cavity 206. Invarious embodiments, the resonant cavity 206 may be defined by a firstreflective structure 208 a and a second reflective structure 208 b. Thegain medium 202 may be arranged between the first reflective structure208 a and the second reflective structure 208 b along an optical axis.The resonant cavity 206 may also be referred to as an optical cavity.

The first reflective structure 208 a may be arranged to reflect lightincident on the first reflective structure 208 a towards the secondreflective structure 208 b along the optical axis and the secondreflective structure 208 b may be arranged to reflect light incident onthe second reflective surface 208 b towards the first reflective surface208 a along the optical axis. In other words, light may bounce betweenthe first reflective structure 208 a and the second reflective structure208 b, passing through the gain medium 204 after each reflection. As thelight passes through the gain medium 204, a wavelength or range ofwavelengths of the light is amplified by stimulated emission.

The first reflective structure 208 a and the second reflective structure208 b may be arranged substantially parallel to each other.

The first reflective structure 208 a may be partially transparent sothat light incident in the first reflective structure 208 a may bepartially transmitted through the first reflective structure 208 a andpartially reflected towards the second reflective structure 208 b alongthe optical axis. The first reflective structure 208 a may be referredto as an optical coupler. The second reflective structure 208 b may be ahighly reflective mirror. The resonant cavity 206 may be defined or mayinclude other suitable arrangements of reflective surfaces. The halidesemiconductor material may be represented by the general formula AMX₃,where A may be a monopositive organic or inorganic ion (e.g. an organicgroup or organic cation or a metal cation or element), M may be adivalent metal cation or element, and X may be a halogen anion orelement. Examples may include CH₃NH₃PbI₃, CH₃NH₃PbBr₃, CH₃NH₃PbBr₂I,CsSnI₃, CsPbI₃, NH₂CH═NH₂PbI₃. The halide semiconductor material may bealternatively represented by A₂MX₆, where A may be a monopositiveorganic or inorganic ion (e.g. an organic group or organic cation or ametal cation or element), M may be a tetravalent metal cation orelement, and X may a halogen anion or element. Examples may includeCs₂SnI₆, (CH₃NH₃)₂SnI₆. The halide semiconductor material may also havethe general formula A_(2+m)M_(m)X_(3m+2), where A may be a monopositiveorganic or inorganic ion (e.g. an organic group or organic cation or ametal cation or element), M may be a divalent metal cation or element,and X may an halogen anion or element (m greater or equal to 1).Examples may include (CH₃NH₃)₃SnI₅, (NH₂CH═NH₂)₂CH₃NH₃SnI₅,(NH₂CH═NH₂)₂CH₃NH₃SnI₂Br₃. The halide semiconductor may instead berepresented by the formula A_(3n−1) M_(n)X_(3n+1), where A may be amonopositive organic or inorganic ion (e.g. an organic group or organiccation or a metal cation or element), M may be a divalent metal cationor element, and X may an halogen anion or element (n greater or equal to1). An example may be (CH₃NH₃)₂CuCl₃Br. In various embodiments, thehalide semiconductor material may include an organic ammonium cation ororganic ammonium cation group. The organic group may be the organicammonium cation or group. The organic ammonium group may be selectedfrom a group consisting of an ammonium group, a hydroxylammonium group,a methylammonium group, a hydrazinium group, a azetidinium group, aformamidinium group, an imidazolium group, a dimethylammonium group, anethylammonium group, a guanidinium group, a group with formula[C_(n)H_(2n+1) NH₃] where 2<n<20 or a long chain group such asphenethylammonium group [(C₆H₅—C₂H₄)NH₃] and combinations thereof. Theorganic ammonium cation may be selected from a group consisting of anammonium ion [NH₄]⁺, a hydroxylammonium ion [H₃NOH]⁺, a methylammoniumion [(CH₃)NH₃]⁺, a hydrazinium ion [H₃N—NH₂]⁺, an azetidinium ion[(CH₂)₃NH₂]+, a formamidinium ion [NH₂(CH)NH₂]⁺, an imidazolium ion[C₃N₂H₅]⁺, a dimethylammonium ion [(CH₃)₂NH₂]⁺, an ethylammonium ion[(C₂H₅)NH₃]⁺, a guanidinium ion [C(NH₂)₃]⁺, a cation with formula[C_(n)H_(2n+1)NH₃]⁺ where 2<n<20 or a long chain ion such asphenethylammonium ion [(C₆H₅—C₂H₄)NH₃]⁺ and combinations thereof. Invarious alternate embodiments, the halide semiconductor material mayinclude a metal cation such as Cs⁺, K⁺, Rb⁺. The halide semiconductormaterial may include a metal such as Cs, K or Rb.

The one or more metal elements may be selected from Group 14 of theperiodic table. The halide semiconductor material may include one ormore metal elements selected from a group consisting of Cu, Pb, Sn, Ge,Eu, Cr, Mn, Ni, Zn, Pd, Cd, Hg, Ba and Sr. The halide semiconductormaterial may include one or more metal cations selected from thecationic 2+ group (e.g. Cu²⁺, Pb²⁺, Sn²⁺ Ge²⁺, Eu²⁺, Cr²⁺, Mn²⁺, Ni²⁺,Zn²⁺, Pd²⁺, Cd²⁺, Hg²⁺, Ba²⁺ and Sr²⁺).

The one or more halogen elements may be selected from Group 17 of theperiodic table. The halide semiconductor material may include one ormore halogen elements selected from a group consisting of F, I, Cl andBr. The halide semiconductor material may include one or more halideanions selected from a group consisting of F⁻, I⁻, Cl⁻ and Br⁻.

Examples of halide semiconductor materials may for instance includeHNC(NH₂)₂SnF₃, C₂H₅NH₃Pb_(0.5)Sn_(0.5)Cl₃, and CH₃NH₃SnFCl₂.

Various embodiments relate to halide semiconductor materials as a gainmedium. Various embodiments relate to the use or the application of lowtemperature solution processed halide semiconductor materials ascoherent light emission gain medium that could be driven by photonsand/or electrons.

The emission source may be configured to generate light, i.e. amplifiedspontaneous emission, spontaneous emission, and/or laser beam. Theemission source may be configured to generate or emit coherent light. Acoherent light may mean a polarized electromagnetic wave at a frequencywhose phase is correlated over a relatively large distance (thecoherence length) along the beam. The coherence length may be more than10 cm or more than 15 cm or more than 20 cm or more than 50 cm or morethan 1 m. The emission source may be configured to generate theamplified spontaneous emission and/or laser beam when energy is suppliedor pumped into the gain medium 202 by the pump source 204.

In the present context, light may be any electromagnetic waves orcombination of electromagnetic waves. In various embodiments, theemission source may be configured to generate light of a wavelength orrange of wavelengths from a range of 250 nm to about 1 mm, e.g. about380 nm to about 1 mm, e.g. from about 390 to about 790 nm. The emissionsource may be configured to generate visible light and/or infraredlight. In other words, lasing wavelengths spanning from the visible tothe infrared may be achieved using this class of materials.

Halide semiconductor materials may have a low trap density. The gainmedium 202 may have a trap density below 10¹⁸ cm⁻³, e.g. below 0.5×10¹⁸cm⁻³, e.g. below 10¹⁷ cm⁻³, e.g. below 0.5×10¹⁷ cm⁻³, e.g. below 10¹⁶cm⁻³. The gain medium may be configured to achieve amplified spontaneousemission (ASE) at a pump fluence substantially equal to or below 50 μJcm⁻², e.g. substantially equal to or below 20 μJ cm⁻², e.g.substantially equal to or below 15 μJ cm⁻², substantially equal to orbelow 14 μJ cm⁻², e.g. substantially equal to or below 12 μJ cm⁻²,substantially equal to or below 10 μJ cm⁻². The threshold pump fluencemay be dependent on the quality of the cavity. The emission source maybe configured to generate light via amplified spontaneous emission(ASE).

The low trap density of halide semiconductor materials may allowamplified spontaneous emission (ASE) in bare films (i.e. without anycavity or optical feedback) to be achieved with the ultralow thresholdpump fluence.

In various embodiments, the halide semiconductor material may have a ASEthreshold carrier density below 10¹⁹ cm⁻³, e.g. below 5×10¹⁸ cm⁻³, e.g.below 2×10¹⁸ cm⁻³ e.g. about 1.7×10¹⁸ cm⁻³.

Halide semiconductor materials may also exhibit high optical stabilityand durability. Halide semiconductor materials may have long rangebalanced electron and hole diffusion lengths that makes it possible toachieve efficient electrical-driven lasing.

In various embodiments, the gain medium 202 may have a bulk trap densitybelow or about 10¹⁷ cm⁻³, e.g. below or about 6×10¹⁶ cm⁻³, below orabout 6×10¹⁶ cm⁻³.

Further, the gain medium may include halide semiconductor materials(e.g. halide perovskite materials) that are solution processable. Asolution processable gain medium has much greater versatility thantraditional gain media for integration with existing silicon basedtechnologies. The halide semiconductor materials may be applied to amuch wider range of optical cavity designs and substrates by methodssuch as spin-coating, dip-coating or dropcasting. Further, halidesemiconductor materials exhibit broadband gain profile. In variousembodiments, the gain medium may have undergone a post film treatment.In various embodiments, the gain medium may further include additives tocontrol trap density. Additives may include metal halides with a genericstructure MI₂, where M represents a metal cation and I represents theiodide anion. Non-limiting examples include PBI₂, SnI₂, SnF₂. Theadditives may be configured to control metal vacancies/oxidation states.Other additives to improve film formation properties may include acidssuch as HCl, HI or other halide derivatives such as CH₃NH₃Cl.

Facile substitution of the metal element and organic component may allowa wide choice of lasing wavelengths. For instance, the material may beor may include CH₃NH₃PbCl₃, CH₃NH₃PbCl_(1.5)Br_(1.5) and/orCH₃NH₃PbCl₂Br. In various embodiments, the halide semiconductor materialmay include more than one organic cation or group. The halidesemiconductor material may include more than one metal cation. Thehalide semiconductor material may include more than one halide anion.The gain medium 202 may include more than one halide semiconductormaterials. For instance, the gain medium 202 may include a mixture ofCH₃NH₃PbCl₃, CH₃NH₃PbCl_(1.5)Br_(1.5) and CH₃NH₃PbCl₂Br

In various embodiments, the halide semiconductor material layer may on asubstrate such as a quartz substrate. In various embodiments, theemission source may include a layer such asCH₃NH₃PbI₃/[6,6]-phenyl-C61-butyric acid methyl ester (PCBM) on or incontact with the halide semiconductor material layer. In variousembodiments, the gain medium may include a substrate and a halidesemiconductor material layer on the substrate. In various embodiments,the gain medium may further include a layer such asCH₃NH₃PbI₃/[6,6]-phenyl-C61-butyric acid methyl ester (PCBM) on thehalide semiconductor material layer.

Various embodiments may find applications in areas such astelecommunication, quantum computing, data storage and reading out (CD,DVD), laser pointer, barcode readers, laser printers, image scanners,laser surgery, industrial laser machining, directed energy weaponry,laser medicine, etc.

FIG. 2B shows a schematic 200 b showing a cross-sectional side view ofan emission source according to various embodiments. The emission sourcemay also include a gain medium 212, the gain medium 212 including ahalide semiconductor material such as a halide perovskite material. Theemission source may further include a pump source 214 configured toprovide energy to the gain medium 212.

The emission source may be or may include an optical pumped bulkperovskite laser according to various embodiments. The halidesemiconductor material may be or may include a three-dimensionalperovskite gain material 212 such as CH₃NH₃PbX₃(X═Cl, Br, I or theircombinations), CsSnI₃(SnF₂)_(x) or any other suitable perovskitematerial. The perovskite gain materials may be contained in an opticalcavity such as a self formed optical cavity or formed by other opticalelements such as partially transmission mirror 218 a and mirroredelement 218 b. The elements 218 a, 218 b may be the reflectivestructures. The mirrored element 218 b may be disposed at one end of thegain material 212 and the partially transmission mirror 218 a may bedisposed at the other end. A suitable pumping source 214 such as aTi:sapphire laser may provide a pumping energy (e.g. at a wavelength of400 nm). The energy may be transmitted through lens 215 and mirror 218 bto energize the perovskite material. The laser output beam 220 may exitthrough the partially reflective mirror 218 a.

FIG. 2C shows a schematic 200 c showing a cross-sectional side view ofan emission source according to various alternate embodiments. Theemission source may also include a gain medium 222, the gain medium 222including a halide semiconductor material such as a halide perovskitematerial. The emission source may further include a pump source 224 a,224 b configured to provide energy to the gain medium 222. The pumpsource 224 a, 224 b may include a first flash tube 224 a and a secondflash tube 224 b arranged on opposing sides of the gain medium 222. Theemission structure may further include partially transmission mirror 228a and mirrored element 228 b. The elements 228 a, 228 b may be thereflective structures.

The emission source shown in FIG. 2C may be referred to as a flash tubeside pumped perovskite laser. The gain medium 222 may be side pumpedusing flash tubes 224 a, 224 b.

FIG. 2D shows a schematic 200 d showing a perspective view an emissionsource according to various alternate embodiments. FIG. 2E shows aschematic 200 e showing a cross-sectional side view of the emissionsource of FIG. 2D according to various embodiments. The emission sourcemay also include a gain medium 232, the gain medium 232 including ahalide semiconductor material such as a halide perovskite material. Theemission source may further include a pump source 234 configured toprovide energy to the gain medium 232. The gain medium 232 may be aperovskite waveguide.

Although we only show bulk lasers with perovskite used as the gainmaterial in the earlier figures, various embodiments may relate also toperovskite channel waveguide laser as shown in FIG. 2D. The perovskitechannel waveguide laser may be conveniently formed on a substrate 235 a(including a material such as silica or aluminum oxide). The perovskitewaveguide 232 may be formed for example, using a suitable lithographicapproach. The channel perovskite waveguide 232 may be covered with anovercoating or cladding layer 235 b, the overcoating or cladding layer235 b including a suitable polymer or dielectric material withrefractive index lower than the perovskite material. The perovskitewaveguide 232 may include two mirrored ends 238 a, 238 b as reflectivestructures. Laser beam 240 may exit the less reflective end 238 a.

FIG. 2F shows a schematic 200 f showing a cross-sectional side view ofan emission source according to various other embodiments. The emissionsource may also include a gain medium 242, the gain medium 242 includinga halide semiconductor material such as a halide perovskite material.The emission source may further include a pump source 244 configured toprovide energy to the gain medium 242. The gain medium 242 may be aperovskite waveguide. The emission source may be or may include a topoptical pumped bulk perovskite Distributed Bragg Reflector (DBR) laser.

The perovskite DBR laser may be on a substrate 245 with periodicstructures 248 a, 248 b serving as gratings to provide optical feedbackfor the emission in the perovskite gain medium 242. Laser beam 250 exitsfrom the top 248 a.

FIG. 2G shows a schematic 200 g showing a cross-sectional side view ofan emission source according to various other embodiments. The emissionsource may also include a gain medium 252, the gain medium 252 includinga halide semiconductor material such as a halide perovskite material.The emission source may further include a pump source 254 configured toprovide energy to the gain medium 252. The gain medium 252 may be aperovskite waveguide. The emission source may be or may include aperovskite Distributed Feedback (DFB) laser.

The emission source may include a substrate 255 a, a diffraction grating255 c on the substrate 255 a. The emission source may further include alaser element 255 a on the diffraction grating 255 c. The diffractiongrating 255 c may include the gain medium 255 c and be configured toreflect light to and from the gain medium 255 c to generate laser beam260. In other words, a periodic structure such as a diffraction grating255 c may be integrated into the active perovskite gain medium 252. Thediffraction grating 255 c may provide optical feedback for the emission.The whole structure may be supported by a substrate 255 a with a laserelement 255 c on top of it. Laser beam 260 may exit from the side.

FIG. 2H shows a schematic 200 h showing a cross-sectional side view ofan emission source according to various other embodiments. The emissionsource may also include a gain medium 262, the gain medium 262 includinga halide semiconductor material such as a halide perovskite material.The emission source may further include a pump source 264 configured toprovide energy to the gain medium 252. The pump source 264 may be or mayinclude an electrical source, such as a power supply 264. The emissionsource may be or may include an electrically pumped perovskite laser(side emitting). The emission source may include a gain medium 262between a first laser element 265 a and a second laser element 265 b. Afirst electrode 267 a may be on the first laser element 265 a and asecond electrode 267 b may be on the second laser element 265 b. Theelectrical source 264 may be electrically coupled to the first electrode267 a and the second electrode 267 b. Electrical energy may be suppliedby the electrical source 264 to generate laser beam 270. In other words,the perovskite laser may also be pumped electrically by connecting anelectrical power source 264 across two electrodes 267 a and 267 b andthe electrons and holes are transported through laser elements 265 a and265 b to provide an electric field across the perovskite gain material262 and provide the necessary population inversion to result in thelasing action that produces output beam 270. The beam 270 may travel ina direction perpendicular to a direction from the first electrode 267 ato the second electrode 267 b.

FIG. 2I shows a schematic 200 i showing a cross-sectional side view ofan emission source according to various other embodiments. The emissionsource may also include a gain medium 272, the gain medium 272 includinga halide semiconductor material such as a halide perovskite material.The emission source may further include a pump source 274 configured toprovide energy to the gain medium 252. The pump source 274 may be or mayinclude an electrical source, such as a power supply 274. The emissionsource may be or may include an electrically pumped perovskite DBR laser(top emitting). The emission source may include a gain medium 272between a first laser element 275 a and a second laser element 275 b. Afirst electrode 277 a may be on the first laser element 275 a and asecond electrode 277 b may be on the second laser element 275 b. Theelectrical source 274 may be electrically coupled to the first electrode277 a and the second electrode 277 b. Electrical energy may be suppliedby the electrical source 274 to generate laser beam 280. The first laserelement 275 a may be a first Distributed Bragg Reflector (DBR) and thesecond laser element 275 b may be a second Distributed Bragg Reflector(DBR). The laser may be pumped electrically by connecting an electricalpower source 274 across two electrodes 277 a, 277 b and the electronsand holes may be transported through laser elements 277 a, 277 b toprovide an electric field across the perovskite gain material 272 andprovide the necessary population inversion to result in the lasingaction. The Distributed Bragg Reflectors 277 a, 277 b may determine thelasing wavelength and the laser beam 280 exits from the less reflectiveend 277 a. The laser beam may travel in a direction parallel to adirection from electrode 277 b to electrode 277 a.

FIG. 3 shows a schematic 300 of a method of forming an emission sourceaccording to various embodiments. The method may include, in 302,providing a gain medium including an halide semiconductor material. Themethod may also include, in 304, providing a pump source configured toprovide energy to the gain medium.

In other words, a method of fabricating a emission source may includeproviding a gain medium including an halide semiconductor material andarranging a pump source so that the pump source is able to provideenergy, e.g. electrical energy and/or optical energy to the gain medium.

In various embodiments, the gain medium may be arranged within aresonant cavity. The gain medium may be arranged within the cavity byarranging the gain medium between a first reflective structure and asecond reflective structure along an optical axis.

In various embodiments, the first reflective structure may be arrangedto reflect light incident on the first reflective structure towards thesecond reflective structure along the optical axis and the secondreflective structure may be arranged to reflect light incident on thesecond reflective surface towards the first reflective surface along theoptical axis.

In various embodiments, the first reflective structure may be partiallytransparent so that light incident in the first reflective structure maybe partially transmitted through the first reflective structure andpartially reflected towards the second reflective structure along theoptical axis.

In various embodiments, the halide semiconductor material may be formedby reacting a metal halide (e.g. PbI₂, SnCl₂, CaBr₂) with an organicammonium halide. The metal halide may be caused to react with theorganic or inorganic halide such as an ammonium halide (e.g. CH₃NH₃I,CH₃NH₃F, HNC(NH₂)₂Br etc.) by mixing the metal halide with the organicammonium halide in a suitable solvent.

While only selected examples are mentioned in the experimental sectionof halide semiconductor material, these examples are not intended to belimiting and other halide semiconductor materials may show similarresults.

In various embodiments, the halide semiconductor material may be formedby dropcasting or spincoating or any other solution-based methods. Thehalide semiconductor material may be formed by printing processes, (e.g.dropcasting or spincoating etc.), physical deposition methods (e.g.thermal evaporation, sputtering etc.) or combinations thereof.

The halide semiconductor material, e.g. organic-inorganic perovskitefilms may be prepared by simple solution deposition processes such asdropcasting and spincoating. The solution may include CH₃NH₃X and PbX₂(where X may be a halogen such as I, Cl, Br and F or mixtures of them)dissolved in an appropriate solvent such as DMF (Dimethyl formamide) orGBL (Gamma butyrylactone). The wt % of the solute (CH3NH₃X+PbX₂) may beas high as 40%, or as high as 35%. Upon deposition and mild heating, thedeposited film may transform into crystalline CH₃NH₃PbX₃. Heatingtemperature may be a temperature less than 100° C., e.g. less than 80°C., e.g. less than 50° C. Another solution based technique may includethe spincoating of PbX₂ on a substrate followed by dipping it in aCH₃NH₃X solution to complete its transformation to CH₃NH₃PbX₃. Othernon-solution based techniques such as evaporative deposition may alsopossible.

Solution processed organic-inorganic perovskite materials may providesimple and inexpensive alternatives to traditional semiconductor gainmediums which were produced with expensive gas-phase methods. Variousembodiments may be easily integrated with existing silicon basedelectronics. If compared with traditional semiconductor gain mediums,various embodiments may also provide better temperature stability of theASE occurring threshold. The low temperature of processing may alsoenable integration of these materials on to flexible substrates.

Low-temperature solution-processed materials that show optical gain andcan be embedded into a wide range of cavity resonators are attractivefor the realization of on-chip coherent light sources. Organicsemiconductors and colloidal quantum dots are considered the maincandidates for this application.

However, stumbling blocks in organic lasing include intrinsic lossesfrom bimolecular annihilation and the conflicting requirements of highcharge carrier mobility and large stimulated emission; whereaschallenges pertaining to Auger losses and charge transport in quantumdots still remain. Herein, we reveal that halide semiconductors such assolution-processed organic-inorganic halide perovskites (CH₃NH₃PbX₃where X D Cl, Br, I) may demonstrate huge potential in photovoltaics andmay have promising optical gain. Their ultra-stable amplifiedspontaneous emission at strikingly low thresholds may stem from theirlarge absorption coefficients, ultralow bulk defect densities and slowAuger recombination. Straightforward visible spectral tunability(390-790 nm) is demonstrated. Importantly, in view of their balancedambipolar charge transport characteristics, these materials may showelectrically driven lasing.

EXPERIMENTAL SECTION

Organic-inorganic halide perovskites have recently emerged as a newclass of photovoltaic materials with high efficiencies driven by thelarge absorption coefficients and long-range balanced electron and holetransport lengths. Surprisingly, we found that they may also exhibitexcellent coherent light emission properties.

The CH₃NH₃PbI₃ films on quartz substrates were prepared by spin-coating10 vol % solutions in DMF. [6,6]-phenyl-C61-butyric acid methyl ester(PCBM) layers were spin-coated from a solvent mixture (10 mg ml⁻¹) ofanhydrous chlorobenzene and anhydrous chloroform (1:1 v/v).

The samples were put in vacuum for more than three days to get rid ofany residual solvent before the optical measurements. Mixed halides wereprepared by blending appropriate molar ratios of CH₃NH₃PbI₃, CH₃NH₃PbBr₃and CH₃NH₃PbCl₃ solutions. The solar cells were fabricated using thesequential deposition procedure, as previously reported andcharacterized under simulated air mass 1.5 global (AM1.5G) solarirradiation in the dark.

Optical spectroscopy. For femtosecond optical spectroscopy, the lasersources were a Coherent Legend regenerative amplifier (150 fs, 1 kHz,800 nm) seeded by a Coherent Vitesse oscillator (100 fs, 80 MHz) and aCoherent Libra regenerative amplifier (50 fs, 1 kHz, 800 nm) seeded by aCoherent Vitesse oscillator (50 fs, 80 MHz). 800 nm wavelength laserpulses were from the regenerative amplifier's output whereas 400 nmwavelength laser pulses were obtained with a BBO doubling crystal.600-nm laser pulses were generated from the Coherent TOPAS-C andCoherent OPerA-Solo optical parametric amplifiers. The laser pulses(circular spot, diameter 1.5 mm) were directed to the films under vacuumin a cryostat. The emission from the samples was collected at abackscattering angle of 150 by a pair of lenses into an optical fibrethat was coupled to a spectrometer (Acton, Spectra Pro 2500i) anddetected by a charge coupled device (Princeton Instruments, Pixis 400B).Time-resolved PL (TRPL) was collected using an Optronis Optoscope streakcamera system which has an ultimate temporal resolution of about 10 ps.All optical measurements were performed at room temperature, except forASE from CH₃NH₃PbCl₃ (at 150 K). Room-temperature photoluminescencequantum yield (PLQY) of the perovskite thin films was measured using anintegrating sphere. The samples were excited with 600 nm pulsesgenerated from the Coherent OPerA-Solo. The emission was corrected forCCD and grating responsivity. Room-temperature gain measurements werecarried out using standard VSL methods. The excitation stripe wasfocused by a cylindrical lens (with focal length f=20 cm) to a stripeand the emission collection configuration was the same as describedabove. The excitation stripe length was varied through an adjustableslit actuated by a micrometer which was placed at the focal line of thecylindrical lens.

After spincoating, a clear optically flat film of CH₃NH₃PbI₃ wasobtained with thickness of about 65 nm. FIG. 4A is a plot 400 a of acomparison of the amplified spontaneous emission (ASE) profile(indicated by 1402) in relation to the absorption (indicated by 1404)and spontaneous emission (SE)/photoluminescence profile (indicated by1406) for CH₃NH₃PbI₃. The ASE develops at the wavelength where theoptical gain and absorption are balanced—the ASE peak is red-shiftedwith respect to the photoluminescence (PL) peak. The CH₃NH₃PbI₃ film hasstrong absorbance (˜10⁴ cm⁻¹) from UV to near infrared (800 nm) with twodistinct peaks located at 480 nm and 760 nm, which are consistent withprevious publications. The broad strong absorbance is a good indicationof its excellent light harvesting capabilities. The second absorptionpeak (760 nm) is attributed to the direct gap transition from the firstvalence band maximum to the conduction minimum. The first absorptionpeak (480 nm) is attributed to the transition from lower valence band tothe conduction band minimum. The strong band edge PL peaks at 770 nm.Absorbance is measured in cm⁻¹ while PL intensity/SE and amplifiedspontaneous emission are in arbitrary units (a.u.). Absorbance, PLintensity/SE and amplified spontaneous emission are plotted againstwavelength (nm).

FIG. 4B shows a plot 400 b of a typical time resolved photoluminescence(TRPL) decay transients following photo-excitation with pump fluencebelow (˜10 μJ cm⁻², indicated by 1406) and above (˜13 μJ cm⁻², indicatedby 1410) the ASE threshold (i.e., 12±2 μJ cm⁻²). FIG. 4B shows thevariation of PL intensity in arbitrary units (a.u.) against time (inps). The lifetime data presented in FIG. 4B is collected over a timewindow of 18 ns to allow consistent comparison with the longer-lived SEdynamics. FIG. 4C is a streak camera image 400 c of spectrum againsttime (collected over a time window of 460 ps) for below ASE thresholdfluence. FIG. 4D is a streak camera image 400 d of spectrum against time(collected over a time window of 460 ps) for above ASE thresholdfluence.

FIG. 8A is a plot 800 a showing steady-state photoluminescence (PL)emission spectra from a 65-nm-thick CH₃NH₃PbI₃ film photoexcited using600 nm, 150 fs and 1 kHz pump pulses with increasing pump fluence (perpulse). FIG. 8A illustrates the transition from spontaneous emission(SE) to amplified spontaneous emission (ASE) with increasing pumpfluence at 1.2 μJ cm⁻², 10 μJ cm⁻², 11 μJ cm⁻², 13 μJ cm⁻², 15 μJ cm⁻²the CH₃NH₃PbI₃ film, which is spin-coated on a quartz substrate.

FIG. 8B is a plot 800 b showing the corresponding time resolvedphotoluminescence (TRPL) intensity measured at 788±10 nm. FIG. 8B showsthe TRPL intensity at a pump fluence of 1.2 μJ cm⁻², 10 μJ cm⁻², 11 μJcm⁻², 13 μJ cm⁻².

FIG. 8C is a plot 800 c full width at half maximum (FWHM) of theemission peak (indicated by 802) and average transient photoluminescencelifetime (τ_(PL)) (indicated by 804) as a function of the pump fluence.τ_(PL) may be defined as the time taken for the intensity to decrease to1/e of its initial value. At low pump levels, the broad spontaneousemission (SE) (with FWHM about 50 nm) from CH₃NH₃PbI₃ increases linearlywith increasing pump fluence. Correspondingly, the average transientphotoluminescence (PL) lifetimes (τ_(PL)) progressively decrease.

FIG. 8D is a plot 800 d showing photoluminescence intensity as afunction of pump fluence. The arrows indicate the trap state saturationthreshold fluence (P_(th) ^(trap)) and the ASE threshold fluence (P_(th)^(ASE)). Line 806 and line 808 represent the linear fits to experimentaldata in the two linear regimes of SE and ASE, respectively. The dashedvertical lines 810 a, 810 b in FIGS. 8C and 8D respectively indicate theonset of ASE.

Above the threshold fluence (12±2 μJ cm⁻²), the emission intensity mayincrease superlinearly (as shown in FIG. 8D), with PL dramaticallyshortened owing to the occurrence of a new short lifetime (<10 ps)dynamical process. Concurrently, the emission band may collapse to yielda sharp peak at 788 nm (as shown in FIG. 8A). These may provide clearsignatures of optical amplification of the SE from CH₃NH₃PbI₃, i.e. ASEbehaviour. The balance between optical gain and self-absorption may giverise to a red-shifted ASE peak that is located near the tail of theabsorption edge (as shown in FIG. 4A).

The intrinsic gain properties of perovskites are investigated byexamining the ASE behaviour in a cavity-free configuration. The ASEvalues provide a better benchmark for comparing different material setson their intrinsic suitability for gain applications.

From the measured threshold fluence (12±2 μJ cm⁻² and absorptioncoefficient (á=5.7×10⁴ cm⁻¹ at 600 nm), the ASE threshold carrierdensity may be calculated to be about 1.7×10¹⁸ cm⁻³. The thresholdcarrier density may correspond to the ease with which a material canattain net gain through optical or electrical generated means.Comparatively, for highly crystalline high-temperature-grown ZnSe andCdS nanowires (with similar α=10⁵ cm⁻¹ at the excitation wavelengths),the typical threshold carrier densities are nearly one order largerunder similar measurement conditions.

Similarly, the typical ASE threshold carrier density forsolution-processed organic thin films may be approximately one orderlarger. As a point of comparison, state-of-the-art cavity-freesolution-processed polymer films such aspoly[9,9-dioctylfluorene-co-9,9-di(4-methoxyphenyl)-fluorene] (F8DP) andSuper Yellow exhibited an ASE threshold of about 6 μJ cm⁻² (calculatedfrom reported threshold pump energy of 0.1 μJ per pulse; excitationstripe about 400 μm×about 4 mm) and about 36 μJ cm⁻² (calculated fromthe reported values of 315 nJ/pulse over a rectangular spot of lengthabout 2.5 mm and width about 350 μm) respectively.

The results on CH₃NH₃PbI₃ also compare favourably to reported CdSe/ZnCdScore/shell colloidal quantum dot (QD) films having an ASE threshold of90 μJ cm⁻².

Photoluminescence quantum yield (PLQY) values approaching 20% at pumpfluence above the ASE thresholds have also measured using an integratingsphere. FIG. 9A is a plot 900 a showing photoluminescence quantum yield(PLQY) (in percentage or %) dependence on pump fluence (in μJ cm⁻²). ThePLQY measurements are carried out for CH₃NH₃PbI₃ films at various pumpfluence at room temperature using an integrating sphere. The sampleswere excited with 600 nm pulses generated from the Coherent OPerA-Solo,an optical parametric amplifier. The emission was corrected for CCD andgrating responsivity.

The room temperature gain of the CH₃NH₃PbI₃ sample was assessed usingVariable Stripe Length (VSL) measurements. FIG. 9B is a plot 900 bshowing room temperature variable stripe length (VSL) measurements ofthe CH₃NH₃PbI₃ films and fitted using the respective methods used forsolution processed colloidal quantum dots thin films. FIG. 9C is a plot900 c showing room temperature variable stripe length (VSL) measurementsof the CH₃NH₃PbI₃ films and fitted using the respective methods used fororganic thin films. FIGS. 9B and 9C show variation of intensity(arbitrary units or a.u.) against stripe length (cm)

The data is fitted using two methods. The method developed by Shakleeand Leheny (Shaklee, K. L. & Leheny, R. F. “Direct determination ofoptical gain in semiconductor crystals.” Appl. Phys. Lett. 18, 475-477(1971)), is a straightforward way to determine the gain spectrum of amaterial over the small signal regime (utilized for inorganic andorganic semiconductors in slab geometry).

The equation is provided by:

$\begin{matrix}{I_{o} = {\frac{I_{S}A}{g}\left\lbrack {{\exp({gz})} - 1} \right\rbrack}} & (1)\end{matrix}$where I_(o)(z), g, and z are the detected light intensity, gaincoefficient and excitation stripe length, respectively; I_(s) is thespontaneous emission rate per unit volume and A is the cross-sectionalarea of the excited volume.

Another method developed by Chan et al. (Chan, Y. et al., Bluesemiconductor nanocrystal laser, Appl. Phys. Lett. 86, 073102 (2005))for analysis over the entire signal regime (including saturation) and ismore commonly used in solution processed colloidal quantum dot films.

The equation is provided by:

$\begin{matrix}{I = {\exp\left\lbrack {{gl}_{a}\left( {1 - {\exp\left\{ \frac{- \left( {z - z_{o}} \right)}{I_{a}} \right\}}} \right)} \right\rbrack}} & (2)\end{matrix}$Wherein I, g, and z are the ASE intensity, gain coefficient andexcitation stripe length. Respectively; while z_(o) accommodates forpossible pump beam inhomogenity and delayed ASE onset. I_(a) is aparameter that accounts for the saturation in ASE intensity which isdefined as the gain lifetime multiplied by the speed of light within thegain medium.

The relatively low yield may be a consequence of the low exciton bindingenergy (19±3 meV) as well as high electron and hole mobilities.Nonetheless, variable stripe length (VSL) measurements on CH₃NH₃PbI₃have revealed a gain of about 250 cm⁻¹ (fitted with Chan's method inChan, Y. et al., Blue semiconductor nanocrystal laser, Appl. Phys. Lett.86, 073102 (2005), typically used for colloidal QDs, see FIG. 4F) orabout 40 cm⁻¹ (fitted with Shaklee and Leheny's method in Shaklee, K. L.& Leheny, R. F. “Direct determination of optical gain in semiconductorcrystals.” Appl. Phys. Lett. 18, 475-477 (1971), largely used for filmsof conjugated polymers, see FIG. 4G) at a pump fluence of 14 μJ cm⁻².The gain values obtained from the respective methods compare favourablywith those for colloidal quantum dots (Dang, C. et al. Red, “green andblue lasing enabled by single-exciton gain in colloidal quantum dotfilms.” Nature Nanotech. 7, 335-339 (2012), Liao, Y., Xing, G., Mishra,N., Sum, T. C. & Chan, Y. “Low threshold, amplified spontaneous emissionfrom core-seeded semiconductor nanotetrapods incorporated into a sol-gelmatrix.” Adv. Mater. 24, 159-164 (2012)) and conjugated polymer thinfilms (Lampert, Z. E., Reynolds, C. L. Jr., Papanikolas, J. M. &Aboelfotoh, M. O. “Controlling morphology and chain aggregation insemiconducting conjugated polymers: the role of solvent on optical gainin” MEH-PPV. J. Phys. Chem. B. 116, 12835-12841 (2012)) at comparableexcitation intensities.

Various embodiments may show better performance than other solutionprocessed systems. Typical competing non-radiative pathways that canrapidly deplete the carrier population and make ASE unfavourable inother solution-processed semiconductors may not be dominant in variousembodiments. The non-radiative pathways may include bulk defects such asvacancies, interstitials, antisites etc.) with fast trapping in the fsand ps timescales, surface traps which typically may require more than100 ps for carrier diffusion through a few tens of nanometers of thematerial, and multi-particle loss mechanisms (such as bimolecularrecombination in organic thin films or Auger recombination in quantumdots).

Following photo-excitation across the CH₃NH₃PbI₃ bandgap (at low pumpfluence where Auger recombination is not dominant), the excited chargecarriers may either relax through bandedge emission or trap-mediatednon-radiative pathways. The former (relaxing through bandgap emission)may give rise to SE with a lifetime (τ₀) of 4.5±0.3 ns (as shown in FIG.8C). An estimate of the bulk and surface trap densities may be madeunder these conditions where trap state recombination is much slowerthan bandedge radiative recombination. The photo-generated chargecarrier density (n_(c)(t)) after photoexcitation may be described with aset of differential equations. The model reveals the presence of twotypes of traps in these CH₃NH₃PbI₃ thin films, with the bulk trapsexhibiting fast trapping times and the surface traps exhibiting slowtrapping times.

FIG. 10A is a plot 1000 a showing room temperature lasing fromCH₃NH₃PbI₃ single crystals from dropcasted films. 1002 indicates thelasing data while 1004 indicates the PL data. FIG. 10B is an opticalmicrograph 1000 b of the crystal. FIG. 10C is a plot 1000 c showing thelasing data 1002 fitted to 5 peaks (indicated by 1006). The mostprominent mode shows a full width half maximum of 1.2 nm. FIGS. 4H, 4Jplot PL intensity (in a.u.) against wavelength (nm).

Under low fluence fs laser pulse excitation (where Auger recombinationis negligible) and the assumption that trap states recombination is muchslower than band edge radiative recombination, the dynamics ofphoto-generated charge carrier density (n_(c)) can be described with thefollowing set of differential equations:

$\begin{matrix}{\frac{{dn}_{c}(t)}{dt} = {{- {\sum\limits_{i}{a_{i}{n_{c}(t)}{n_{TP}^{i}(t)}}}} - \frac{n_{c}(t)}{\tau_{0}}}} & (3) \\{\frac{{dn}_{TP}^{i}(t)}{dt} = {{- {a_{c}(t)}}{n_{TP}^{i}(T)}}} & (4)\end{matrix}$Wherein n_(TP) ^(i)(t) is the trap states density and a_(i) is theproduct of the trapping cross section and the carrier velocity.Therefore the first term in equation (3) represents varioustrap-mediated non-radiative pathways, while the second term denotes theradiative recombination inside the film. Thus the relationship betweenthe integrate bandedge PL intensity (I_(PL)=k∫₀ ^(∞)n_(c)(t)/τ₀dt, wherek is a constant) the initial photogenerated charge carrier densityn_(e)(0) can be obtained as:

$\begin{matrix}{{n_{c}(0)} = {{\sum\limits_{i}{{n_{YTP}^{i}(0)}\left( {1 - e^{{- a_{i}}\tau_{0}{I_{PL}/k}}} \right)}} + {I_{PL}/k}}} & (5)\end{matrix}$Fitting the experimental result with equation (5) yields two types oftraps in these CH₃NH₃PbI₃ thin films, with the bulk(surface/interfacial) traps exhibiting fast (slow) trapping times. Thebulk trap density n_(TP) ^(F) is about 5×10¹⁶ cm⁻³ while thesurface/interfacial trap density n_(TP) ^(S) is about 1.6×10¹⁷ cm⁻³.This correlates well with a simple estimation of the total trap density(bulk and surface) obtained by the intersection of the linearlyextrapolated PL intensity (indicated by line 806) with that of the pumpfluence axis from FIG. 8D (i.e. n_(TP) ⁰˜2×10¹⁷ cm⁻³). This intersectionrepresents the pump fluence needed to fill all the traps (i.e., thethreshold trap pump fluence P_(th) ^(Trap)).

FIG. 10D is a plot 1000 d showing photoluminescence (PL) intensity as afunction of photon-generated exciton density within the low pump fluencerange. The experimental data can be well-fitted (R²=0.99) with equation(5) for two types of trapping states.

The bulk trap density (n_(TP) ^(F)) is about 5×10¹⁶ cm⁻³ whereas thesurface trap density (n_(TP) ^(S)) is about 1.6×10¹⁷ cm⁻³. The trapdensities measured in CH₃NH₃PbI₃ may be comparable to defect densitiesin highly ordered organic crystals (10¹⁵-10¹⁸ cm⁻³) and superior tothose of solution-processed organic thin films (10¹⁹ cm⁻³).Solution-deposited, high-temperature annealed Cu—In—Ga—S/Se (CIGS)chalcogenide layers also exhibit comparable defect densities to thatreported here (10¹⁶ cm⁻³). These low bulk defect densities in perovskiteare also consistent with the high solar cell efficiencies in thismaterial.

Finite difference time domain (FDTD) simulations (Lumerical™ FDTDsoftware) were performed to evaluate the optical confinement effects ofthe PCBM layer. The structure includes Quartz (100 nm)/CH₃NH₃PbI₃ (65nm)/[6,6]-phenyl-C61-butyric acid methyl ester (PCBM) (45nm-optional)/vacuum (390 nm).

FIG. 5A is a plot 500 a showing the real part (n) and imaginary part orextinction coefficient (k) of the complex refractive index. Therefractive index of CH₃NH₃PbI₃ was measured using anellipsometer-n_(CH3NH3PbI3)=2.3 and k_(CH3NH3PbI3)=0.15 at 790 nm whilethat of [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) was extractedfrom the literature (Hoppe, H., Sariciftci, N. S., & Meissner, D.Optical constants of conjugated polymer/fullerene basedbulk-heterojunction organic solar cells, Mol. Cryst. Liq. Cryst. 385,233-239 (2002)).

FIG. 5B shows a schematic 500 b of the of a gain medium 502 undersimulation conditions according to various embodiments. The gain medium502 may be on a quartz film 504. The gain medium 502 may includeCH₃NH₃PbI₃ film. A PCBM layer 506 may be on the gain medium 502. A lightsource 508 (e.g. yellow line) may be introduced in-plane to the gainmedium 502 and perfectly matched layers (PML) boundary conditions 510 a,510 b may be used to absorb the incident light at the top and bottomedges with minimal reflections. A vacuum 512 may be between the top PML510 a and the structure including the gain medium 502.

FIG. 5C is a schematic 500 c showing intensity distributions in the y-zplane of structures of light polarized parallel to the structuresurface. 514 shows the intensity distribution of the light in the y-zplane of a structure with quartz film 504, gain medium 502 on quartzfilm 504 and PCBM layer 506 on the gain medium. 516 shows the intensitydistribution of the light in the y-z plane of a structure with quartzfilm 504 and gain medium 502 on quartz film 504, i.e. without PCBM layer506.

To examine the effects of the more prevalent surface traps on thecarrier dynamics and ASE, PL measurements on bare CH₃NH₃PbI₃ werecompared against CH₃NH₃PbI₃/[6,6]-phenyl-C61-butyric acid methyl ester(PCBM), C60) bilayers to mimic the presence of infinite interfacialelectron trap states. Selective excitation of the CH₃NH₃PbI₃ layer(about 65 nm thick for both cases) was performed with 600 nm laserpulses.

FIG. 11A is a plot 1100 a showing the time-integrated PL spectra ofCH₃NH₃PbI₃ (indicated by 1102) and CH₃NH₃PbI₃/([6,6]-phenyl-C61-butyricacid methyl ester (PCBM) (indicated by 1104). FIG. 11B is a plot 1100 bshowing the time-resolved photoluminescence (TRPL) decay transients forquartz/CH₃NH₃PbI₃ (about 1.3 μJ cm⁻², indicated by 1106),quartz/CH₃NH₃PbI₃/PCBM (about 1.3 μJ cm⁻², indicated by 1108 and about17 μJ cm⁻², indicated by 1110) films in vacuum following excitation at600 nm (1 kHz, 150 fs). Through modifying the surface/interfacial trapdensity, these measurements reveal that, whereas SE is strongly quenchedby the surface/interfacial traps, ASE—which occurs on a much fastertimescale—could effectively compete with these carrier trappingprocesses. The solid lines in FIG. 11B are the single-exponential fitsof the PL decay transients. FIG. 11C is a plot 1100 c of the pumpfluence-dependent photoluminescence spectra of quartz/CH₃NH₃PbI₃ (65nm)/PCBM film. FIG. 11D is a plot 1100 d of the photoluminescenceintensity of quartz/CH₃NH₃PbI₃ (65 nm)/PCBM film. The line 1112represents the linear fit to experimental data in the linear regime ofSE. The line 1114 represents the linear to experimental data in thelinear regime of ASE.

The presence of the PCBM layer (˜45 nm) is expected to severely quenchthe SE from the CH₃NH₃PbI₃ layer; see FIG. 11A for the PL spectra andFIG. 11B for the PL decay transients. Such efficient PL quenchingoriginates from the long-range electron diffusion in the CH₃NH₃PbI₃film, where the diffusion-limited electron trapping time by the surfacestates can be estimated to be about 0.40 ns (Xing, G. et al. Long-rangebalanced electron- and hole-transport lengths in organic-inorganicCH₃NH₃PbI₃. Science 342, 344-347 (2013).). Surprisingly, under high pumpfluence excitation, the ASE is impervious to the presence of the PCBMlayer, which acts as a perfect electron quencher.

FIG. 11B clearly shows that the carrier avalanche proceeds at a muchfaster timescale than the carrier trapping at the surface states. Thusthe surface states will not affect the ASE processes, only the fast bulktraps. Indeed, the ASE threshold fluence for the CH₃NH₃PbI₃/PCBM film ismeasured to be 10±2 μJ cm⁻² (FIG. 11D).

This value is slightly smaller than that of the bare CH₃NH₃PbI₃ film(12±2 μJ cm⁻²) (shown in FIG. 8D) because of the better lightconfinement and propagation due to the presence of the PCBM claddinglayer which improves gain buildup.

FIG. 7A is a schematic 700 a of a solar cell according to variousembodiments. The solar cell may include a substrate 702 such as fluorinedoped tin oxide (FTO) glass. The solar cell may further include ablocking layer 704 on the substrate 702. The blocking layer 704 may be atitanium oxide (TiO₂) blocking layer. The solar cell may further includea mesoporous layer 706 (e.g. a TiO₂ mesoporous layer) on the blockinglayer 704. The solar cell may further include a layer including halideperovskite material 708 (e.g. CH₃NH₃PbI₃) on the mesoporous layer 706.The solar cell may additionally include a hole transport layer 710 onlayer 708. The solar cell may also include an electrode 712 (e.g. a goldor aluminum electrode) on the hole transport layer 710. FIG. 7B is aplot 700 b showing the current density J (mA cm⁻²) under A 1.5 (100mW/cm²) illumination. FIG. 7C is a plot 700 c of photoluminescence (PL)intensity (arbitrary units) as a function of pump fluence (μ J cm⁻²)showing amplified spontaneous emission (ASE) threshold of the solar cellconfiguration. FIG. 7D is a plot 700 d of the ASE spectrum. Thephotoluminescence (PL) intensity (arbitrary units) as a function ofwavelength (nm). FIG. 7E is a plot 700 e showing ASE photostabilitymeasured under ambient conditions of the device (Excited with 600 nm, 1KHz, 50 fs laser pulses, ˜20 μJ cm⁻²). FIG. 7F is a photo 700 f showinga demonstration of green ASE from CH₃NH₃PbBr₃ deposited on PETsubstrates pumped using two-photon absorption at 800 nm.

Remarkably, ASE can also be observed in functional photovoltaic devices(ç=11.4%; Device structure: FTO/TiO₂ compact layer/TiO₂ mesoporouslayer/CH₃NH₃PbI₃/Spiro-OMeTAD/Au) with optical excitation; see FIG. 7A.The presence of the Spiro-OMeTAD layer, which acts as a perfect holequencher, has no effect on the ASE from CH₃NH₃PbI₃—further exemplifyingits exceptional gain properties.

Although a low bulk defect density is favourable for obtaining reducedASE thresholds, a critical criterion for achieving ASE is suppressedmulti-particle non-radiative recombination rates (for example,bimolecular recombination noted in organics or Auger recombination ininorganic semiconductors). Bimolecular recombination (which is alimiting process in organic lasing) has been reported to be extremelylow in CH₃NH₃PbI₃—defying the Langevin recombination limit by at leastfour orders of magnitude.

These low bi-molecular charge recombination constants are consistentwith our findings of low bulk defect densities as discussed earlier. TheAuger recombination process in perovskite, which manifests under highpump fluence (nonlinear regime), typically yields Auger lifetimes(τ_(Auger)) from a few ps to ns, depending on the photo-generated chargecarrier density. The Auger recombination in CH₃NH₃PbI₃ is efficient(τ_(Auger)˜300 ps) compared with SE (4.5±0.3 ns) because of thelong-range electron-hole diffusion lengths within them. However, thetimescale for the occurrence of ASE (<10 ps-limited by the instrumentresponse) signifies that the carrier build-up time for populationinversion and the subsequent avalanche, out-competes the Auger processesin these CH₃NH₃PbI₃ thin films (Supplementary Information). In contrastto solution-processed colloidal QDs (typical biexciton τ_(Auger)˜50 psfor 5 nm diameter CdSe QDs), such an Auger loss mechanism is lessdominant in this ‘bulk-like’ CH₃NH₃PbI₃ film.

Temperature dependent studies were also performed to furthercharacterize the solution-processed CH₃NH₃PbI₃ gain medium. FIG. 6A is aplot 600 a of pump fluence dependent photoluminescence (PL) spectra at6K. FIG. 6A plots PL intensity (in arbitrary units or a.u.) againstwavelengths (nm). FIG. 6B is a plot 600 b of pump fluence dependentphotoluminescence (PL) intensity at 6K. FIG. 6B plots PL intensity (inarbitrary units or a.u.) against pump fluence (μJ cm⁻²).

Due to the limited bound states in the film, the emission intensity ofthese two peaks exhibit clear saturation behaviors at higher pumpfluence. However, the free exciton emission intensity increasescontinually with increasing pump fluence, finally achieving ASE above athreshold fluence of 10±2 0/cm². This ASE threshold at 6 K is comparableto that at 300 K (i.e., 12±2 μJ cm⁻²). Comparatively, traditionalinorganic semiconductor gain media are highly susceptible to temperatureinduced effects: strong phonon assisted charge carrier trapping;temperature dependent exciton dissociation and photo-generated chargecarrier diffusion and dilution. Hence, the threshold pump fluence forgenerating coherent light emission from these inorganic semiconductormaterials are strongly temperature dependent. However, for CH₃NH₃PbI₃,the ASE threshold is almost temperature-insensitive, which are similarto organic chromophores and quantum dots. The line 602 represents thefit to experimental data in the regime of SE for the 746 nm PL peak. Theline 604 represents the fit to experimental data in the regime of ASEfor the 746 nm PL peak. Line 606 indicates variation of PL intensity forthe 782 nm peak as a function of pump fluence. Thetemperature-insensitivity of CH₃NH₃PbI₃ ASE threshold stems from itsextremely low trap states density and almost temperature invariantcharge carrier diffusion as indicated by FIG. 6C.

FIG. 6C is a plot 600 c showing time resolved photoluminescence (TRPL)TRPL decay transients for quartz/CH₃NH₃PbI₃ (65 nm) (indicated by 608)and quartz/CH₃NH₃PbI₃ (65 nm)/PCBM(45 nm) (indicated by 610) films invacuum following excitation at 600 nm (1 KHz, 150 fs, ˜1 μJ cm⁻²). Thesolid lines in FIG. 6C are the single-exponential fits of the PL decaytransients.

Our experiments also show that such perovskite gain media have nearlytemperature independent threshold pump fluence (carrier density). Incontrast, traditional semiconductor gain media have strong temperaturedependent threshold pump fluence (carrier density).

The photostability of the CH₃NH₃PbI₃ thin films was assessed bymonitoring the ASE intensity as a function of time under laserirradiation at a 1 kHz repetition rate at room temperature.

FIG. 12A is a plot 1200 a showing shot-dependent ASE intensity of thesolution-processed CH₃NH₃PbI₃ film with over 9×10⁷ laser excitationshots at 600 nm (1 kHz, 50 fs, ˜18 μJ cm⁻²) performed at roomtemperature. The ASE intensity has a standard deviation of 0.2% aboutthe mean intensity for about 26 h of continuous irradiation (that is˜10⁸ laser shots in all). FIG. 12B is a plot 1200 b showingshot-dependent ASE intensity of the solution processed CH₃NH₃PbI₃ andCH₃NH₃PbI₃/PCBM films over 7×10⁶ at 600 nm (1 KHz, 50 fs, 14 μJ/cm²)under room temperature. Following such a large number of laser pulseexcitation events, the near invariance of the output intensity shown inFIGS. 12A-B bear testimony to the excellent optical stability of the lowtemperature solution processed perovskites as gain media.

This performance compares favourably against the state-of-the-artorganic semiconducting thin films (50% drop in output power after about10⁷ laser shots; Grivas, C. & Pollnau, M. “Organic solid-stateintegrated amplifiers and lasers”, Laser Photon. Rev. 6, 419-462 (2012))and colloidal QDs (50% drop in output power after about 10⁶ laser shots;Chan, Y. et al. “Blue semiconductor nanocrystal laser”, Appl. Phys.Lett. 86, 073102 (2005)). The impressive ASE stability of the perovskitelayers is also evident from tests of perovskite solar cells irradiatedfor about 8 h under ambient conditions (FIG. 7E).

FIG. 12C is a plot 1200 c showing the PL spectrum at 10 K. The dottedlines are the deconvolved Gaussian peaks. The dashed lines in the falsecolour temperature-dependent PL map show the evolution of the emissionpeaks with temperature. FIG. 12D is a plot 1200 d showing widewavelength tunability of ASE wavelengths from low-temperaturesolution-processed organic-inorganic halide perovskite films fabricatedby mixing the precursor solutions.

In the absence of any significant defect concentrations, the SE mayoriginate from the bandedge emission. Because the SE may provide theseed photons for the photon cascade in ASE, the ASE wavelengths may bein turn dependent on the bandgap of the semiconducting film. This isclearly evident from our temperature-dependent studies, where anincrease in the bandgap due to a tetragonal to orthorhombic phasetransition results in a blue-shifted SE and a corresponding shift in theASE (FIG. 12C). The orthorhombic phase may give rise to three emissionpeaks, attributed to two bound exciton emissions (815 nm and 782 nm) anda free exciton emission (746 nm), which yields the low-temperature ASEpeak (at a threshold fluence of 10±2 μJ cm⁻². Such an intrinsicdependence of the ASE on the bandgap may allow wavelength tunabilitythrough halide substitution. By using either mixtures of bromides andiodides or chlorides and iodides, the bandgap may be continuouslytunable over the entire visible spectral range (from about 390 to about790 nm). We realize this through a simple physical mixing of theprecursor solutions before spin-coating.

FIG. 12D is a plot 1200 d showing the ASE from CH₃NH₃PbCl₃,CH₃NH₃PbCl_(1.5)Br_(1.5), CH₃NH₃PbBr₃, CH₃NH₃PbBrI₂ and CH₃NH₃PbI₃ thinfilms, demonstrating its wide wavelength-tunability. The ability of theperovskites to encompass the full visible spectrum may allow them toaddress the ‘green gap’ seen in III-nitrides and III-phosphides. Lasingin perovskites may be achieved with a suitably designed cavity resonator(for example, with microspheres as whispering galley mode lasing or withgratings as distributed feedback lasing). Towards this lasing has alsobeen observed from CH₃NH₃PbI₃ single crystals from dropcast thin films(FIGS. 10A-C). This shows that despite the relatively lower PLQYmeasured, the impressive gain, the large absorption cross-section, lowdefect densities, low bimolecular recombination and slow Augerrecombination in CH₃NH₃PbI₃ enables lasing.

FIG. 13A is a plot 1300 a showing the time-integrated PL spectrameasured at 760±10 nm for quartz/CH₃NH₃PbI₃(65 nm) (indicated by line1302 a), quartz//CH₃NH₃PbI₃ (65 nm)/PCBM (indicated by 1304 a),quartz/CH3NH3PbI3(65 nm)/Spiro-OMeTAD (indicated by 1306 a) films invacuum following excitation at 600 nm (1 KHz, 150 fs, 1.3 μJ cm2). FIG.13B is a plot 1300 b showing TRPL decay transients measured at 760±10 nmfor quartz/CH3NH3PbI3(65 nm) (indicated by line 1302 b),quartz/CH3NH3PbI3(65 nm)/PCBM (indicated by line 1304 b),quartz/CH3NH3PbI3(65 nm)/Spiro-OMeTAD (indicated by line 1306 b) filmsin vacuum following excitation at 600 nm (1 KHz, 150 fs, 1.3 μJ/cm²).The solid lines in FIG. 13B are the single-exponential fits of the PLdecay transients. FIG. 13C is a plot 1300 c of exciton diffusion lengthas a function of PL lifetime quenching ratios. FIG. 13C is based onequation (5). Diffusion length is scaled in multiples of CH₃NH₃PbI₃layer thickness (L=65 nm). A consequence of the low trap density withinthis perovskite gain medium may include long range balanced electron andhole diffusion lengths, which guarantee the good electron and holeinjection. It may therefore possible to achieve efficientelectrical-driven lasing in this class of materials.

Various embodiments may be fabricated using a low temperature solutionprocessed approach. In contrast, traditional semiconductor gain mediaare usually produced at elevated temperatures and using high vacuumgrowth techniques that require significant infrastructural investments.

Further, a solution processable gain medium according to variousembodiments may have much greater versatility than traditional gainmedia for integration with existing silicon based technologies. It maybe applied to a much wider range of optical cavity designs andsubstrates by simply spin-coating, dip-coating or dropcasting.

The lasing wavelength in these classes of materials may be determined bythe band to band transition. The energetic separation between the bands(and hence the lasing wavelength) can be modified by facile substitutionof either the metal or the organic component or the halide. This canallow lasing wavelengths from the visible to the infrared.

Our findings show that these organic-inorganic halide semiconductors maybe a new class of robust solution-processed gain media with highlydesirable characteristics. The low ASE threshold and the long-rangebalanced charge carrier diffusion length may stem from the low bulkdefect density in CH₃NH₃PbI₃ films. The highly crystalline PbX₆three-dimensional network may lend crystalline inorganic character toCH₃NH₃PbX₃ while maintaining its solution processability. Broadwavelength tunability is possible with both cation and anionreplacement. Their low-temperature solution processing may be highlycompatible with unconventional substrates, printing technologies andmonolithic integration with silicon-based electronics. Together with thelong-range balanced electron and hole diffusion, high charge carriermobilities and low bimolecular charge recombination rates, as well aslarge wavelength range continuously tunable coherent emission, ourfindings indicate that the simple solution-processed CH₃NH₃PbX₃ may holdthe key to realizing electrically driven solution-processed on-chipcoherent light sources.

Low temperature solution processed photovoltaics suffer from lowefficiencies due to poor exciton/electron-hole diffusion lengths(typically about 10 nanometers). Recent reports of highly efficientCH₃NH₃PbI₃-based solar cells in a broad range of configurations raise acompelling case for understanding the fundamental photophysicalmechanisms in these materials. By applying femtosecond transient opticalspectroscopy to bilayers that interface this perovskite with eitherselective electron or selective hole extraction materials, we haveuncovered concrete evidence of balanced long-range electron-holediffusion lengths of at least 100 nm in solution processed CH₃NH₃PbI₃.The high photoconversion efficiencies of these systems stem from thecomparable optical absorption length and charge carrier diffusionlengths, transcending the traditional constraints of solution processedsemiconductors.

An ideal solar cell material should combine good optical absorptioncharacteristics with efficient charge transport properties. Lowtemperature solution processed light harvesting films prepared bytechniques such as spin coating and chemical bath deposition aretypically amorphous or poorly crystalline, consequently suffering frompoor charge carrier transport. This limitation necessitates devicedesigns that decouple light absorption and charge carrier transportlengths, including light trapping strategies such as plasmonics as wellas the sensitized solar cell architecture. The recent development oforganic-inorganic halide perovskite materials such as CH₃NH₃PbI₃ aslight harvesters in solid state sensitized solar cells has led toreports of impressive efficiency values of up to 15%. This remarkablematerial has been employed in a variety of photovoltaic architectures. Aconfiguration employed by Kim et al. (H. S. Kim et al., “Lead iodideperovskite sensitized all-solid-state submicron thin film mesoscopicsolar cell with efficiency exceeding 9%”, Scientific Reports 2, 591(2012)) and Heo et al. (J. H. Heo et al., Efficient inorganic-organichybrid heterojunction solar cells containing perovskite compound andpolymeric hole conductors. Nature Photonics 7, 486 (2013)), sandwichesthe thin perovskite layer between a rough mesoporous TiO₂ photoanode anda hole transporting layer such as(2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamine)-9,9′-spirobi-fluorene(Spiro-OMeTAD). Lee et al. (M. M. Lee, J. Teuscher, T. Miyasaka, T. N.Murakami, H. J. Snaith, “Efficient hybrid solar cells based onmeso-superstructured organometal halide perovskites”, Science 338, 643(2012)) have shown that efficient solar cells can be fabricated byreplacing the TiO₂ photoanode with an insulating Al₂O₃ scaffold—implyinggood electron transport properties. Surprisingly, Etgar et al. (L. Etgaret al., Mesoscopic CH₃NH₃PbI₃/TiO₂ heterojunction solar cells. Journalof the American Chemical Society 134, 17396 (2012)) reported anefficiency of 5.5% in a configuration without the hole transportinglayer—indicating good hole transport properties. These indications ofambipolar charge transport capabilities are supported by a recent reportby Ball et al. (J. M. Ball, M. M. Lee, A. Hey, H. J. Snaith,Low-temperature processed mesosuperstructured to thin-film perovskitesolar cells. Energy and Environmental Science 6, 1739 (2013)) whichdemonstrated that ˜350 nm thick planar films sandwiched between a TiO₂compact layer and a hole transporting layer can generate short circuitcurrent densities of 15 mA/cm². These reports together imply that theelectron and hole transport lengths within these organic-inorganichybrid materials are high. Nonetheless, the innate dynamics of thephotoexcited electrons and holes in CH₃NH₃PbI₃ driving the highefficiencies in these solar cells are unknown. Herein, throughfemtosecond transient optical spectroscopy of CH₃NH₃PbI₃ heterojunctionswith selective electron and hole extraction, we successfully decoupleelectron and hole dynamics and show clear evidence of long electron andhole transport lengths (both over 100 nm). Our findings indicate thatthis class of materials does not suffer from the bottleneck of lowcollection lengths which handicap typical low temperature solutionprocessed photovoltaic materials.

FIG. 14A is am illustration 1400 a showing the absorbance andtransmission spectra of CH₃NH₃PbI₃, CH₃NH₃PbI₃/PCBM,CH₃NH₃PbI₃/Spiro-OMeTAD. 1410 shows the absorbance spectra for pureCH₃NH₃PbI₃. 1420 shows the differential transmission spectra forCH₃NH₃PbI₃. 1430 shows the differential transmission spectra forCH₃NH₃PbI₃/PCBM. 1440 shows the differential transmission spectra forCH₃NH₃PbI₃/Spiro-OMeTAD. The films are in vacuum and the spectra aremeasured at 600 nm (1 KHz, 150 fs, 13 μJ/cm²). Lines 1422, 1432, 1442are measured at 1 ps. Lines 1424, 1434, 1444 are measured at 100 ps.Lines 1426, 1436, 1446 are measured at 500 ps. Lines 1428, 1438, 1448are measured at 1 ns.

FIG. 14B is an illustration 1400 b showing normalized bleaching kineticsfor films in vacuum following excitation at 600 nm (1 KHz, 150 fs, 1.3μJ/cm²). 1450 shows the normalized bleaching kinetics at 480 nm while1460 shows the normalized bleaching kinetics at 760 nm. 1452, 1462represent the data for CH₃NH₃PbI₃. 1454, 1464 represent the data forCH₃NH₃PbI₃/PCBM. 1456, 1466 represent the data forCH₃NH₃PbI₃/Spiro-OMeTAD.

FIG. 15A is an illustration 1500 a of normalized bleaching kinetics inshort time range showing the inter-valence band hot hole cooling forCH₃NH₃PbI₃ (in vacuum) following excitation. 1510 shows the early timedynamics following excitation at 400 nm (1 μJ/cm²). 1520 shows the earlytime dynamics following excitation at 600 nm (1.3 μJ/cm²). 1512, 1522represent the data at 480 nm while 1514, 1524 represent the data at 760nm.

FIG. 15B is a schematic 1500 b illustrating the hot hole cooling andcharge recombination within CH₃NH₃PbI₃ and charge separation at theCH₃NH₃PbI₃/PCBM and CH₃NH₃PbI₃/Spiro-OMeTAD interfaces. The approximatepositions of VB1 and VB2 were obtained from the TA measurements.

FIG. 16 is a schematic 1600 of the energy levels of the heterojunctionsand depiction of the exciton generation, diffusion and quenchingprocesses in the respective bilayers.

FIG. 17 is a plot 1700 showing step profiles of the thickness of theCH₃NH₃PbI₃, CH₃NH₃PbI₃/PCBM and CH₃NH₃PbI₃/Spiro-OMeTAD films. 1702shows the step profile of CH₃NH₃PbI₃ film. 1704 shows the step profileof CH₃NH₃PbI₃/PCBM film. 1706 shows the step profile ofCH₃NH₃PbI₃/Spiro-OMeTAD film.

FIG. 18 is a cross-sectional transmission electron microscopy image 1800of a typical trilayer showing the clear interfaces between theperovskite and the electron and hole acceptor layers. FIG. 19 is a plot1900 of absorption coefficient of CH₃NH₃PbI₃ as a function ofwavelength—calculated from equation (6).

FIG. 20 is a schematic 2000 showing 4 possible scenarios for the twopeaks (480 nm and 760 nm) observed in the linear absorption and TAspectra.

FIG. 21 is a plot 2100 showing normalized probe wavelength dependentkinetics for CH₃NH₃PbI₃ film in vacuum following excitation at 600 nm(0.7 μJ/cm²). The signals at 640 nm and 700 nm were reversed for bettercomparison. Note the zero crossing of the signals at timescale below 1ps for the 700 nm probe. This signature is characteristic of hot chargecarrier cooling in the short timescales. 2102 is measured at 480 nm,2104 is measured at 640 nm, 2106 is measured at 700 nm and 2108 ismeasured at 760 nm.

FIG. 22 is a plot 2200 showing normalized pump fluence dependentkinetics at 760 nm for CH₃NH₃PbI₃ film vacuum following excitation at600 nm. 2202 represents a pump fluence of 0.7 μJ/cm², 2204 represents apump fluence of 1.3 μJ/cm², 2206 represents a pump fluence of 2.6μJ/cm², and 2208 2204 represents a pump fluence of 6.5 μJ/cm²,

FIG. 23 is an illustration 2300 showing pump fluence dependent dynamicsfor CH₃NH₃PbI₃ (lines 2314 a, 2316 a, 2318 a, 2322 a, 2324 a, 2326 a,2328 a) and CH₃NH₃PbI₃ (dots 2314 b, 2316 a, 2318 b, 2322 b, 2324 b,2326 b, 2328 b) in vacuum. 2310 shows the pump fluence dependentdynamics at 480 nm while 2320 shows the pump fluence dynamics at 760 nm.2322 a, 2322 b are for a pump fluence of 0.7 μJ/cm². 2314 a, 2314 b,2324 a, 2324 b are for a pump fluence of 1.3 μJ/cm². 2316 a, 2316 b,2326 a, 2326 b are for a pump fluence of 2.6 μJ/cm². 2318 a, 2318 b,2328 a, 2328 b are for a pump fluence of 6.5 μJ/cm².

FIG. 24 is a plot 2400 showing pump fluence dependent relative PLquantum yield with 600 nm, 150 fs and 1 KHz laser pulse excitation. 2402shows the data for CH₃NH₃PbI₃/PCBM while 2404 shows the data forCH₃NH₃PbI₃/Spiro-OmeTAD.

FIG. 25 is a table 2500 showing relative photoluminescence (PL) quantumyield (ç_(PL)), PL decay time (τ_(PL)), TA decay time (τ_(TA)) and theestimated charge transfer time (τ_(CT)) from the TA results.

In this study, electron extraction layers (such as[6,6]-phenyl-C61-butyric acid methyl ester (PCBM), C60) with conductionband levels below that of CH₃NH₃PbI₃ and hole extraction layers (such asSpiro-OMeTAD, poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate)(PEDOT:PSS)) with valence band levels above CH₃NH₃PbI₃ were interfacedto CH₃NH₃PbI₃ to permit decoupling of the electron and hole dynamics(FIG. 16). Comparing measurements on bare CH₃NH₃PbI₃ againstCH₃NH₃PbI₃/hole acceptor bilayers and CH₃NH₃PbI₃/electron acceptorbilayers enables identification of electron and hole signatures in theorganic/inorganic halide.

Under identical experimental conditions, the photoluminescence (PL)quantum yield of the 65 nm thick CH₃NH₃PbI₃ is greatly reduced when theperovskite is interfaced with an electron extracting PCBM layer or ahole extracting Spiro-OMeTAD layer (FIG. 13A). The PL intensity isquenched by a factor of 12.5 in the bilayer with Spiro-OMeTAD and by afactor of 50 in the bilayer with PCBM (FIG. 25). Given that the currentconfigurations are ideal layered systems (FIG. 17 and FIG. 18), thesehigh degrees of PL quenching, comparable to closely blendeddonor/acceptor system, are particularly revealing. Given a linearabsorption coefficient of 5.7×10⁴ cm⁻¹ at 600 nm (1410 in FIG. 14A, FIG.19), near homogenous generation of the charge carriers in these 65 nmCH₃NH₃PbI₃ layers can be ensured. The PL quenching is expected tooriginate from the charge carrier extraction across the interface.

Efficient PL quenching suggests that the charge carrier diffusion lengthinside the CH₃NH₃PbI₃ layer is comparable to or longer than the layerthickness (65 nm). Correspondingly, the PL lifetimes were alsosignificantly shortened when CH3NH3PbI3 was interfaced with the PCBM orSpiro-OMeTAD layer (FIG. 13B)—with fitted lifetimes of 4.5 (±0.3) ns,0.37 (±0.02) ns and 0.64 (±0.03) ns for the CH₃NH₃PbI₃, CH₃NH₃PbI₃/PCBMand CH₃NH₃PbI₃/Spiro-OMeTAD, respectively. The single exponential PLdecay indicates the good crystalline quality of the samples. Using therelation (1/τ_(Heterojunction)=1/τ_(Perovskite)+1/τ_(CT)), the chargecarrier transfer times τ_(CT) (and efficiency) can be estimated to be0.40 ns (92%) and 0.75 ns (86%) for CH₃NH₃PbI₃/PCBM andCH₃NH₃PbI₃/Spiro-OMeTAD, respectively. The slight variation between thecharge carrier transfer efficiencies obtained using steady state PL(FIGS. 13A, 25) and transient PL can be attributed to: (i) extremelyfast charge carrier transfer at the interface (that cannot be monitoredat the current temporal resolution); and (ii) the dependence of thesteady state PL on the light reflection, scattering and refraction bythe additional PCBM and Spiro-OMeTAD layers in the heterojunctions.Next, a charge carrier extraction model based on diffusion was employedto estimate the charge carrier diffusion lengths. FIG. 13C shows thedependence of the charge carrier diffusion length on the PL lifetimequenching ratios obtained from the analytical solution of the model.Assuming that charge carrier quenching occurs only at the extractionlayer interface with 100% efficiency, minimum estimates of the extractedelectron and hole diffusion lengths are 130 nm and 90 nm. By comparison,solution processed organic conjugated materials have typical diffusionlengths about 10 nm; thermally deposited organic molecules have typicaldiffusion lengths of 10-50 nm; and colloidal quantum dot films havediffusion lengths ˜30 nm (organic cross-linked) and ˜80 nm (hybridsurface passivated). Thus the conservatively estimated long diffusionlengths in the low temperature solution processed CH₃NH₃PbI₃ filmscompare favorably.

To improve the accuracy of these estimated values from the direct PLapproach and obtain more details on the photo-excited charge carrierdynamics, complementary transient absorption spectroscopy (TAS)measurements were also performed. Due to the large absorptioncoefficients and the long charge carrier diffusion lengths, low pumpfluence is essential to avoid extensive Auger recombination inCH₃NH₃PbI₃—see FIGS. 21 to 24. 1410 in FIG. 14A shows the linearabsorption spectrum of CH₃NH₃PbI₃ spanning the UV to near infrared (800nm) with two distinct peaks located at 480 nm and 760 nm, in agreementwith earlier publications. The second absorption peak (760 nm) isattributed to the direct gap transition from the first valence bandmaximum (VB1) to the conduction band minimum (CB1). However, the originof the first absorption peak (480 nm) is still unresolved.

Representative TA spectra of CH₃NH₃PbI₃ and its bilayer counterpartsover the same spectral region are shown in 1420, 1430, 1440 (FIG.14A)—with two pronounced photo-bleaching (PB) bands. These long-lived PBpeaks are located at almost the same spectral positions as the twoabsorption peaks. The PB at 480 and 760 nm are labeled as PB1 and PB2,respectively, and are attributed to state-filling. For 600 nmphoto-excitation, it is reasonable to attribute the 760 nm PB2 band tostate filling effects (which include the hole population of VB1, theelectron population of CB1 and the inter-band stimulated emission).

However, it is not straightforward to assign the transitions associatedwith the 480 nm PB1 band. Given that the photo-excitation energy (of˜2.06 eV for 600 nm wavelength) is smaller than the energy of the PB1peak (2.58 eV), only one of the two energy states involving this PBtransition could be populated. The long-lived nature of this PB bandfurther suggests that the populated energy level should be either VB1 orCB1 (see SM for a more detailed discussion of the assignment).

Upon selective excitation of the CH₃NH₃PbI₃ layer, no new PB orphotoinduced absorption bands are observed when the electron or holeextraction layer is present. A comparative study at the respective probewavelengths of PB1 and PB2 would thus yield detailed information aboutthe charge carrier dynamics. For pure CH₃NH₃PbI₃, the recombinationdynamics at different probe wavelengths are relatively invariant over arange of pump fluences where second order effects are insignificant(FIG. 21). All these decay transients are well-fitted with a singleexponential time constant of 5.6 (±0.1) ns, which is longer than themeasured PL lifetime of 4.5 (±0.3) ns (FIG. 25). As time-resolved PLcannot monitor the recombination dynamics of all the photo-excitedcarriers, this finding suggests that the PL lifetime in pure CH₃NH₃PbI₃is limited by the minority carrier lifetime. Correlating these PLlifetimes with the TA lifetimes of the bilayers allows us to identifythe minority charge carriers. With the PCBM (electron acceptor) layerpresent, both PB1 and PB2 bleaching peaks show an additional fastlifetime component of 0.37 (±0.02) ns (FIG. 14B), which is closelymatched to the measured PL lifetime. This suggests that electrons arethe minority charge carriers in CH₃NH₃PbI₃. Since PB1 and PB2 dynamicsare simultaneously affected by the electron extraction layer, the probesmonitor the electron population in the CB1. For theCH₃NH₃PbI₃/Spiro-OMeTAD (hole acceptor) samples, only PB2 exhibits anadditional fast decay lifetime of 0.59 (±0.03) ns (1450, FIG. 14B),which is slightly faster than the PL lifetime of 0.64 (±0.03) ns (FIG.25). This indicates that PB2 also reflects the hole population of VB1(i.e., the transitions between VB1 and CB1). PB1 on the other hand isonly related to the electron population in CB1 (i.e., the transitionsbetween the lower valence band (VB2) and CB1) (FIG. 15B). By comparingthe PB1 decays between pure CH₃NH₃PbI₃ and CH₃NH₃PbI₃/PCBM, wedetermined electron extraction time and efficiency values inCH₃NH₃PbI₃/PCBM to be 0.40 ns (±0.05) and 68%. 1450 (FIG. 14B) alsoshows that about 27% of the photo-generated electrons are possiblytrapped, and therefore contribute neither to the electron extractionfrom CH₃NH₃PbI₃ to PCBM, nor to the radiative recombination. Bycomparing the decay at PB2 between pure CH₃NH₃PbI₃ andCH₃NH₃PbI₃/Spiro-OMeTAD, we estimate the hole extraction time inCH₃NH₃PbI₃/Spiro-OMeTAD to be 0.66 (±0.05) ns.

However, given that the TA signal at PB2 is a combination of signalsfrom both electrons and holes, it is difficult to estimate the detailedhole extraction efficiency at this stage. The origins of PB1 and PB2suggest the possibility of hot holes cooling from VB2 to VB1 followingexcitation of CH₃NH₃PbI₃ across the VB2-CB1 gap. Such hot hole coolingdynamics could be validated through varying the pump wavelengths.

After 3.10 eV (400 nm) excitation, 1510 (FIG. 15) shows a very fastbleach buildup for PB1 which is close to the 150 fs laser pulseduration. Subsequently, hole localization from VB2 to VB1 occurs (within˜0.4 ps). The decay of the PB1 transient (indicative of the depopulationof VB2) is well-matched with a concomitant rise of the bleach signal atPB2 (indicative of VB1 being populated)—both at 0.4±0.1 ps. On the otherhand, excitations with lower energy photons (e.g. across the VB1-CB1 gapusing 2.07 eV (600 nm) pulses), do not excite carriers in VB2 andtherefore, such hot hole cooling dynamics are absent (FIG. 3B). This 0.4ps hot hole cooling is much slower than that in most organicsemiconductors (˜100 fs). Potentially, these hot hole energies could beefficiently extracted before the hot holes cool down to VB1 throughoptimizing the device configuration.

From fitting the TA decay dynamics with the diffusion model, theelectron and hole diffusion coefficients were found to be 0.036 and0.022 cm2/s, respectively. Using these values, the electron and holediffusion lengths (L_(D)) perpendicular to the film surface werecalculated to be L_(D) ^(c)=130 nm and L_(D) ^(h)=110 nm whereL_(D)=√{square root over (Dτ_(TA))}. As expected, the L_(D) ^(h)(majority carrier diffusion length) determined here is longer than thatextracted from the more direct PL approach presented earlier, which issensitive to the minority carrier dynamics. The long transport lengthsassociated with CH₃NH₃PbI₃ are linked to its crystal structure, whichincludes corner-connected PbI₆ octahedra that form a three-dimensionalframework.

Other organic/inorganic halide materials based on Sn have also displayedgood charge transport properties. The slightly shorter diffusion lengthof the holes compared to the electrons is consistent with the hole'slarger effective mass and larger positive space charge limitedtransport. Nonetheless, these values are relatively balanced as comparedto typical values reported in bulk heterojunction solar cells where theelectron and hole transport lengths (proportional to their mobility)differ by orders of magnitude resulting in space charge limitedphotocurrents. These balanced long charge carrier diffusion lengthswould account for the remarkable performances reported for theseCH₃NH₃PbI₃ devices.

These L_(D) values are underestimated mainly because of the assumptionthat no quenching at the CH₃NH₃PbI₃-quartz or -vacuum interfaces occur.The measured carrier lifetimes, τ₀ are more susceptible to thenon-ideality of these interfaces in these thinner spincoated CH₃NH₃PbI₃layers, leading to smaller τ₀ and consequently shorter LD. Measurementsin more “bulk-like” samples would yield longer τ₀ and higher L_(D)(submicron)—FIG. 13C. From the linear absorption coefficients (1410,FIG. 14A), the absorption lengths are L_(a)˜100 nm (at ë=500 nm). Theseconservatively estimated carrier diffusion lengths measured inCH₃NH₃PbI₃ are comparable to the optical absorption lengths for λ≤500nm, but are shorter than the absorption lengths at longer wavelengths.Increasing the optical thickness of these layers through light trappingarchitectures compensates for this slight mismatch—accounting for thehigh photoconversion efficiencies reported in these systems.

Methods and Materials. [6,6]-phenyl-C61-butyric acid methyl ester (PCBM)layers were spincoated from a solvent mixture (10 mg/ml) of anhydrouschlorobenzene and anhydrous chloroform (1:1 v/v) while PEDOT:PSSemployed in the study was Clevios™ A1 4083) layer.(2,2′,7,7′-tetrakis(N,-di-p-methoxyphenylamine)-9,9-spirobifluorene)(Spiro-OMeTAD) films were prepared by spincoating 20 mg/ml solutions inchlorobenzene. The CH₃NH₃PbI₃ films were prepared by spincoating 10 wt %solutions in anhydrous DMF. The samples were stored in vacuum for morethan 3 days to rid them of any residual solvent before the opticalmeasurements. FIG. 16 shows the schematic energy levels of the donor andacceptors materials utilized in this work. The thickness of the studiedfilms was determined with Step-Profile measurements (FIG. 17) andmatches well with values extracted from TEM imaging (FIG. 18).

All optical measurements were conducted in an optical cryostat undervacuum. For femtosecond optical spectroscopy, the laser source was aCoherent Legend™ regenerative amplifier (150 fs, 1 KHz, 800 nm) that wasseeded by a Coherent Vitesse™ oscillator (100 fs, 80 MHz). 800 nmwavelength laser pulses were from the regenerative amplifier's outputwhile 400 nm wavelength laser pulses were obtained through doubling thefundamental 800 nm pulses with a BBO crystal. 600-nm laser pulses weregenerated from a Light Conversion TOPAS-C optical parametric amplifier.The emission from the samples was collected at a backscattering angle of150° by a pair of lenses and into an optical fiber that is coupled to aspectrometer (Acton, Spectra Pro 2500i) to be detected by a chargecoupled device (CCD) camera (Princeton Instruments, Pixis 400B).Time-resolved PL was collected using an Optronis Optoscope™ streakcamera system which has an ultimate temporal resolution of ˜10 ps. Forfemtosecond TA experiments, the samples were pumped at 2.07 eV (or 3.1eV) and probed with a white-light continuum. The probe pulses (420-820nm) were generated by focusing a small portion (˜5 μJ) of thefundamental 800 nm laser pulses into a 2 mm-thick sapphire plate. Thelinear polarization of the pump pulse was adjusted to be perpendicularto that of the probe pulse with a polarizer and a half waveplate. Thecross-polarization will eliminate any contribution from coherentartifacts at early times. Pump-induced changes of transmission (DT/T) ofthe probe beam were monitored using a monochromator/PMT configurationwith lock-in detection. The pump beam was chopped at 83 Hz and this wasused as the reference frequency for the lock-in amplifier.

The optical transmittance and total reflectance spectra of CH₃NH₃PbI₃ onquartz substrate and blank quartz substrate were measured with aUV-VIS-NIR spectrophotometer (Shimadzu UV-3600) with an integratingsphere (ISR-3100). The absorption coefficient of the ultrathinCH₃NH₃PbI₃ film was calculated using the following expression:

$\begin{matrix}{\alpha_{film} = {{\frac{d_{sub}}{d_{tot}}\frac{1}{d_{film}}{\ln\left( \frac{1 - R_{tot}}{T_{tot}} \right)}} - {\frac{1}{d_{sub}}{\ln\left( \frac{1 - R_{sub}}{T_{sub}} \right)}}}} & (6)\end{matrix}$where R_(sub), T_(sub) and d_(sub) are the substrate reflectance,transmittance and thickness, respectively. R_(tot), T_(tot) and d_(tot)are reflectance, transmittance and thickness of the substrate/filmsystem, respectively. d_(film) is the CH₃NH₃PbI₃ film thickness. Withequation (6), the interface effect between substrate and film can betaken into account.

Diffusion Model. The charge carrier diffusion lengths (LD) in the activelayer can be estimated using a simple diffusion limited quenching modelin a bilayer system. The laser pulse generated charge carrier density inthe active layer can be described by a one-dimensional diffusionequation:

$\begin{matrix}{\frac{\partial{n\left( {z,t} \right)}}{\partial t} = {{D\frac{\partial^{2}{n\left( {z,t} \right)}}{\partial x^{2}}} - {{kn}\left( {z,t} \right)}}} & (7)\end{matrix}$where n(z, t) is the charge carrier density, D is the charge carrierdiffusion coefficient, k is the original charge carrier consumption ratewithout the acceptor layer. The spatial coordinate z represents thevertical distance of a point in the active layer from the quartz/activelayer interface. With fs laser pulse excitation, the initialphoto-generated charge carrier distribution in the active layer can beexpressed as:n(z,0)=n(0)e ^(−αz)  8where ä is the linear absorption coefficient of the active layer at theexcitation wavelength. Assuming that the donor/acceptor interface is theonly quenching interface with infinite quenching rate, a minimumestimate of L_(D) will be obtained. Solving Equation 7 with the initialcharge carrier distribution and boundary conditions yields the timedependent charge carrier distribution (n(z, t)) and total charge number(N(t)) within the active layer:

$\begin{matrix}{{n\left( {z,t} \right)} = {2n_{0}{\exp\left( {- {kt}} \right)}{\sum\limits_{m = 0}^{\infty}\left( {{\exp\left( {{- \frac{\pi^{2}D}{L^{2}}}\left( {m + \frac{1}{2}} \right)^{2}t} \right)}\frac{{\left( {- 1} \right)^{m}{\exp\left( {{- \alpha}\; L} \right)}{\pi\left( {m + \frac{1}{2}} \right)}} + {\alpha\; L}}{\left( {\alpha\; L} \right)^{2} + {\pi^{2}\left( {m + \frac{1}{2}} \right)}^{2}}{\cos\left( {{\pi\left( {m + \frac{1}{2}} \right)}\frac{z}{L}} \right)}} \right)}}} & (9) \\{{N(t)} = {\frac{2n_{0}L}{\pi}{\exp\left( {- {kt}} \right)}{\sum\limits_{m = 0}^{\infty}\left( {{\exp\left( {{- \frac{\pi^{2}D}{L^{2}}}\left( {m + \frac{1}{2}} \right)^{2}t} \right)}\frac{{{\exp\left( {{- \alpha}\; L} \right)}{\pi\left( {m + \frac{1}{2}} \right)}} + {\left( {- 1} \right)^{m}\alpha\; L}}{\left( {\left( {\alpha\; L} \right)^{2} + {\pi^{2}\left( {m + \frac{1}{2}} \right)}^{2}} \right)\left( {m + \frac{1}{2}} \right)}} \right)}}} & (10)\end{matrix}$where L is the active layer thickness.

Interpretation for Photobleaching (PB) Peaks at 480 nm and 760 nm.

From the linear absorption spectrum in FIG. 19, the PB peaks couldoriginate from one of the four possible scenarios as shown in FIG. 20(A): separate valence bands to separate conduction bands transitions(i.e., VB1→CB1 and VB2→CB2); (B) common valence band to separateconduction bands transitions (i.e., VB1→CB1 and VB1→CB2); (C) separatevalence bands to common conduction band transitions (i.e., VB1→CB1 andVB2→CB1); and (D) a mixture of two photo-systems with independenttransitions. Energy band alignments could be a type I or type IIconfiguration.

Scenario A: The long-lived nanosecond PB transient measured at 480 nmwould exclude this situation because hot carrier relaxation to the lowerlevels would occur on a much faster picoseconds timescale.

Scenario D: The schematic represents a general situation where the bandalignment could be either (a) a type I band alignment where the smallerbandgap system is located within the wider bandgap system; or (b) a typeII band alignment where the energy bands of the two systems arestaggered. Nonetheless, the following discussion is applicable. For the600 nm pump pulse to yield two bleaching peaks at PB1 and PB2, a chargetransfer from the smaller bandgap system (760 nm) to the larger bandgapsystem (480 nm) must have taken place. A key signature of such chargetransfer is a concomitant decrease in the 760 nm probe signal with arise in the 480 nm probe signal over the same time frame. This is notobserved, thus eliminating Scenario D altogether.

Differentiating Scenario B and C: In Scenario B, the dependence of thedynamics at the two wavelengths could be described by:

$\begin{matrix}{{\frac{\Delta\; T}{T}\left( {760\mspace{14mu}{nm}} \right)} = {{k_{1}n_{e}} + {k_{2}n_{h}}}} & (11) \\{{\frac{\Delta\; T}{T}\left( {480\mspace{14mu}{nm}} \right)} = {k_{3}n_{h}}} & (12)\end{matrix}$where k₁, k₂ and k₃ are proportionality constants and n_(e) and n_(h)are the electron and hole populations at CB1 and VB1. The transition at480 nm does not depend on n_(e) since the hot electron at CB2 decayswithin 1 ps.In Scenario C, the dependence of the dynamics at the two wavelengthscould be described by:

$\begin{matrix}{{\frac{\Delta\; T}{T}\left( {760\mspace{14mu}{nm}} \right)} = {{k_{1}n_{e}} + {k_{2}n_{h}}}} & (13) \\{{\frac{\Delta\; T}{T}\left( {480\mspace{14mu}{nm}} \right)} = {k_{3}n_{e}}} & (14)\end{matrix}$where k₁, k₂ and k₃ are proportionality constants and n_(e) and n_(h)are the electron and hole populations at CB1 and VB1.

For the CH₃NH₃PbI₃/PCBM bilayer, the dynamics originating from ne willbe affected; while for the CH₃NH₃PbI₃/Spiro-OMeTAD bilayer, the dynamicsoriginating from n_(h) will be affected. Experimentally, both 480 nm(PB1) and the 760 nm (PB2) transients are modulated in the presence ofthe electron accepting PCBM—indicating that the CB1 is participating inboth the transitions. In addition, only the 760 nm transition (PB2) isaffected by the presence of the hole accepting Spiro-OMeTAD—indicatingthat VB2 is participating in this transition. This eliminates Scenario Band confirms Scenario C.

Second Order Effects—Auger Recombination. It was found that thesecarrier dynamics are strongly pump fluence dependent due to the largelight absorption coefficient (˜5.7×10⁴ cm⁻¹ at 600 nm (FIG. 19) and longcharge carrier diffusion length in CH₃NH₃PbI₃. For pump fluence ≤1.3μJ/cm², multi-particle Auger recombination process in CH₃NH₃PbI₃ isinsignificant and the TA decay transients are identical to thosepresented earlier (FIGS. 21, 22). However, for a pump fluence >2.6μJ/cm² (i.e., photo-generated exciton density >3.7×10¹⁷/cm³), Augerrecombination will dominate over the linear recombination, resulting ina shortening of the TA lifetimes. The existence of Auger recombinationunder these relatively low exciton densities points towards an extremelylong exciton-exciton or exciton-charge interaction length (˜μm) inCH₃NH₃PbI₃—consistent with the long carrier diffusion lengths determinedin this work. Under high pump fluence, the lifetime shortening inducedby the interface charge carrier extraction in the bilayers will beovershadowed by the lifetime shortening caused by Auger recombination(FIG. 23). Therefore, careful regulation of the pump fluence in theultrafast optical spectroscopy of CH₃NH₃PbI₃ is essential for uncoveringits intrinsic properties. As shown in FIG. 24, the relative PL quantumyields (η_(PL)) of CH₃NH₃PbI₃/PCBM and CH₃NH₃PbI₃/Spiro-OMeTAD toCH₃NH₃PbI₃ layer are strongly dependent on the pump fluence used. Atrelative low pump fluence (where Auger recombination is insignificant),η_(PL), is independent of the pump fluence. However, when Auger effectsbecome more dominant, η_(PL) increases with pump fluence. The variationof η_(PL) with pump fluence is more obvious for CH₃NH₃PbI₃/Spiro-OMeTADthan for CH₃NH₃PbI₃/PCBM. This is attributed to the slower holediffusion compared to the electron diffusion in CH₃NH₃PbI₃—consistentwith the hole's larger effective mass and larger space charge limitedtransport. All our PL measurements were performed in the linear rangewith low pump fluence.

While the invention has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims. The scope of the invention is thusindicated by the appended claims and all changes which come within themeaning and range of equivalency of the claims are therefore intended tobe embraced.

The invention claimed is:
 1. An emission source comprising: a gainmedium that provides optical amplification, the gain medium comprising athree-dimensional halide perovskite material; and a pump sourceconfigured to provide energy to the gain medium comprising thethree-dimensional halide perovskite material so that the gain mediumgenerates a coherent stimulated light to emit a laser beam and the gainmedium generates amplified spontaneous emission based on the energyprovided, wherein the three-dimensional halide perovskite material is ahalide semiconductor material, and wherein the gain medium has a trapdensity below 10¹⁸ cm⁻³.
 2. The emission source according to claim 1,wherein the pump source is an optical source configured to provide lightas energy to the gain medium.
 3. The emission source according to claim1, wherein the pump source is an electrical source configured to provideelectrical energy to the gain medium.
 4. The emission source accordingto claim 1, the emission source further comprising: a resonant cavity,the gain medium arranged within the resonant cavity; wherein theresonant cavity is defined by a first reflective structure and a secondreflective structure, the gain medium arranged between the firstreflective structure and the second reflective structure along anoptical axis.
 5. The emission source according to claim 4, wherein thefirst reflective structure is arranged to reflect light incident on thefirst reflective structure towards the second reflective structure alongthe optical axis and the second reflective structure is arranged toreflect light incident on the second reflective surface towards thefirst reflective surface along the optical axis.
 6. The emission sourceaccording to claim 4, wherein the first reflective structure ispartially transparent so that light incident in the first reflectivestructure is partially transmitted through the first reflectivestructure and partially reflected towards the second reflectivestructure along the optical axis.
 7. The emission source according toclaim 1, wherein the three-dimensional halide perovskite materialcomprises an organic ammonium cation.
 8. The emission source accordingto claim 7, wherein the organic ammonium cation is selected from a groupconsisting of an ammonium ion, a hydroxylammonium ion, a methylammoniumion, a hydrazinium ion, an azetidinium ion, a formamidinium ion, animidazolium ion, a dimethylammonium ion, an ethylammonium ion, aphenethylammonium ion, a guanidinium ion, a cation with formula[C_(n)H_(2n+1) NH₃]⁺ where 2<n<20 and combinations thereof.
 9. Theemission source according to claim 1, wherein the three-dimensionalhalide perovskite material comprises one or more metal cations selectedfrom a cationic 2+ group.
 10. The emission source according to claim 1,wherein the three-dimensional halide perovskite material comprises oneor more halide anions selected from a group consisting of F⁻, I⁻, Cl⁻and Br⁻.
 11. The emission source according to claim 1, wherein theemission source is configured to generate light of a wavelength from arange of about 250 nm to about 1 mm.
 12. The emission source accordingto claim 1, wherein the gain medium has undergone a post film treatment.13. The emission source according to claim 1, wherein the gain mediumfurther comprises additives to control trap density.
 14. The emissionsource according to claim 1, wherein the three-dimensional halideperovskite material comprises a three-dimensional organic-inorganichalide perovskite material.
 15. The emission source according to claim1, wherein the three-dimensional halide perovskite material isrepresented by general formula AMX₃, where A is a monopositive organicor inorganic ion, M is a divalent metal cation or element, and X is ahalogen anion or element.
 16. The emission source according to claim 1,wherein the emission source is operable at room temperature.
 17. Theemission source according to claim 1, wherein amplified spontaneousemission occurs above a threshold pump fluence of 10 μJ cm⁻² at 300 K.18. The emission source according to claim 1, wherein thethree-dimensional halide perovskite material is CsSnI₃.
 19. The emissionsource according to claim 1, wherein the gain medium comprises SnF₂. 20.The emission source according to claim 1, wherein the gain medium has atrap density below 10¹⁷ cm⁻³.
 21. The emission source according to claim1, wherein the gain medium has a trap density below 10¹⁶ cm⁻³.
 22. Amethod of forming an emission source, the method comprising: providing again medium that provides optical amplification, the gain mediumcomprising a three-dimensional halide perovskite material; and providinga pump source configured to provide energy to the gain medium comprisingthe three-dimensional halide perovskite material so that the gain mediumgenerates a coherent stimulated light to emit a laser beam and the gainmedium generates amplified spontaneous emission based on the energyprovided, wherein the three-dimensional halide perovskite material is ahalide semiconductor material, and wherein the gain medium has a trapdensity below 10¹⁸ cm⁻³.
 23. The method according to claim 22, whereinthe gain medium is arranged within a resonant cavity by arranging thegain medium between a first reflective structure and a second reflectivestructure along an optical axis.
 24. The method according to claim 23,wherein the first reflective structure is arranged to reflect lightincident on the first reflective structure towards the second reflectivestructure along the optical axis and the second reflective structure isarranged to reflect light incident on the second reflective surfacetowards the first reflective surface along the optical axis.
 25. Themethod according to claim 23, wherein the first reflective structure ispartially transparent so that light incident in the first reflectivestructure is partially transmitted through the first reflectivestructure and partially reflected towards the second reflectivestructure along the optical axis.
 26. The method according to claim 22,wherein the three-dimensional halide perovskite material is formed byreacting a metal halide with an organic or inorganic halide.
 27. Themethod according to claim 22, wherein the three-dimensional halideperovskite material is formed by printing processes, physical depositionmethods or combinations thereof.
 28. The method according to claim 22,wherein the three-dimensional halide perovskite material comprises athree-dimensional organic-inorganic halide perovskite material.
 29. Themethod according to claim 22, wherein the three-dimensional halideperovskite material is represented by general formula AMX₃, where A is amonopositive organic or inorganic ion, M is a divalent metal cation orelement, and X is a halogen anion or element.
 30. The method accordingto claim 22, wherein the emission source is operable at roomtemperature.
 31. The method according to claim 22, wherein amplifiedspontaneous emission occurs above a threshold pump fluence of 10 μJ cm⁻²at 300 K.
 32. The method according to claim 22, wherein thethree-dimensional halide perovskite material is CsSnI₃.
 33. The methodaccording to claim 22, wherein the gain medium comprises SnF₂.
 34. Themethod according to claim 22, wherein the gain medium has a trap densitybelow 10¹⁷ cm⁻³.
 35. The method according to claim 22, wherein the gainmedium has a trap density below 10¹⁶ cm⁻³.